#### 3.1. Characteristics of MicP Concentrations in Japanese Rivers

Figure 2 and

Table A1 show the MicP numerical and mass concentration data from 70 rivers and 90 sites across Japan. Although Kataoka et al. [

40] focused on only three types of MicP materials (PE, polyethylene; PP, polypropylene; PS, polystyrene), all plastic types were included in this study. As a result, the MicP numerical concentration was widely distributed over four orders of magnitude, from 0.03 to 63.89 (particles/m

^{3}), with mean and median values of 4.34 and 1.51 (particles/m

^{3}), respectively. The MicP mass concentration changed over a wide range, from 0.00008 to 16.15 (mg/m

^{3}), with mean and median values of 0.79 and 0.12 (mg/m

^{3}), respectively. The coefficient of variation was 1.85 for the MicP numerical concentration and 2.40 for the MicP mass concentration, indicating that variation of the mass concentration was larger than that of the numerical concentration. The mean MicP size obtained in this study was 1–2 mm. PE, PP, and PS were the dominant plastic types in the MicPs collected.

Figure 3 shows the percentiles of the numerical concentration of MicP,

C_{n}, and mass concentration,

C_{m}. The mean values of both

C_{n} and

C_{m} are larger than their respective median values. The percentage of sites above the mean value was 30% for

C_{n} and 23% for

C_{m}. Moreover, a number of sites with values less than 1/10 of the mean value were also observed, as much as 21% and 46% for

C_{n} and

C_{m}, respectively. From these values, it is apparent that high MicP concentrations at relatively few sites skewed the means.

The correlation between

C_{n} and

C_{m} are shown in

Figure 4. The results from all 90 sites are displayed. Although some variation was observed between the behaviors of

C_{n} and

C_{m}, the approximately straight line that fits the data has a positive slope. The Pearson’s correlation coefficient,

R^{2}, of this line was 0.748, with a

p-value < 0.05, indicating a significant correlation between these two concentrations.

#### 3.2. Relationship between MicP Concentrations and Basin Characteristics

We examined the relationship between the MicP concentrations and basin characteristics utilizing extensive MicP concentration data. The mean values of the urban area ratio at sites above and below the mean MicP mass concentration were 40% and 10%, respectively. However, the mean value of the farmland fraction was 17% both above and below the mean value. A similar trend was observed for the MicP numerical concentration. The MicP concentrations tended to be higher in rivers with larger urban area ratios. Reflecting this, and similar to Kataoka et al. [

40], we plotted the correlation between the MicP concentrations and basin characteristics (population density and urban area ratio,

Figure 5). This figure indicates that the relationship between these concentrations and basin characteristics may be linearly approximated at a 95% confidence interval. The y-axis at a certain value of

x (

Figure 5a, left) is given by the following equations [

54]:

where

n is the number of samples (90),

t_{0.05} is the

t-value (1.987) corresponding to a probability of 5% on both sides of

n = 90 (degrees of freedom: 89),

s is the expected value of the regression residual,

S_{xx} and

S_{yy} are the sums of squares of the deviations from the mean values (

$\overline{x}$ and

$\overline{y}$) for

x and

y, respectively, and

S_{xy} is the sum of the product of the deviations from

$\overline{x}$ and

$\overline{y}$.When these values are divided by

n − 1,

S_{xx} and

S_{yy} become the variances of

x and

y, respectively, and

S_{xy} becomes the covariance of

x and

y.

By inspecting the relationship between

C_{n} and

C_{m}, as well as the population density,

W_{p}, and urban area ratio,

W_{u}, we confirmed that all four values were positively correlated. The following linear approximations were obtained for the respective values:

The correlation coefficient and p-value for each approximation formula are provided above. From these results, it is clear that p < 0.05 for all equations, demonstrating that there was a significant positive correlation between the MicP concentrations and basin characteristics at a 5% confidence interval. The correlation coefficients were greater with W_{u} than with W_{p}.

It is important to note that, as shown in

Figure 5, the observed raw data exhibited some variations, mainly due to the uncertainties in field sampling of the MicPs and the behavior of MicP in rivers (i.e., settling on the riverbed). To reduce some of the variation in MicP, moving average values for the observed raw data are also displayed in

Figure 5. Here, the data were rearranged in order of population density (or urban area ratio), and the 20 adjacent data points were averaged to determine the moving average. The raw population density and urban area ratio data were non-uniform. In other words, the raw data were concentrated within a relatively small population density and urban area ratio, thereby affecting the linear approximation. In order to avoid the problems associated with such a skewed distribution, a moving average was used. As a result of this operation, the moving average of

C_{n} and

C_{m} revealed an increasing trend with both population density and urban area ratio. However, the trend was not linear, instead forming a convex curve. This relationship was observed more distinctly with population density.

We tested several functions to find the approximate curve for the moving average. As a result, the following two piecewise equations were obtained for the population density:

Although a logarithmic function was the most suitable for predicting the moving average of the MicP concentration shown in

Figure 5a, it became negative as the x-axis approached zero. Thus, it was not appropriate to use this function for the entire range. For this reason, a logarithmic function was used here for the range above a certain threshold value,

W_{pth}, and a linear function was used for the range below

W_{pth}. We selected 181 (persons/km

^{2}) as

W_{pth} so that the intercept of the linear function was non-negative and the difference between the two functions at the threshold value was minimized. The correlation coefficients (

R^{2}) for Equations (13–14) were 0.004, 0.912, 0.652, and 0.849 (from top to bottom). Only one low coefficient was observed, but the other approximate curves had favorable

R^{2} values, thus indicating their goodness of fit.

The y-intercept of the approximate curve for the moving average was smaller than that of the approximately straight line for the raw data, suggesting that the approximate curve represents more appropriate values. We selected a quadratic function as an approximate curve for the moving average values for the urban area ratio and obtained the following equations:

In the expression of the MicP mass concentration obtained using the least-squares method, the intercept became negative; thus, we manually set the intercept to 0. Meanwhile, the correlation coefficients for Equations (15) and (16) had values of 0.966 and 0.980, respectively, indicating a better correlation than that of the population density. This improvement over the population density was similar to the results of the linear approximation shown in Equations (9)–(12).

#### 3.3. Calculated Results for Water Balance Analysis

Our water balance model allowed us to determine Japanese plastic emissions, as well as the MicP concentration.

Appendix A Figure A1 shows a nationwide map of the annual values of precipitation,

P, evapotranspiration,

E, surface runoff,

Q_{s}, and underground infiltration,

Q_{i}, obtained via the water balance analysis. Here, the quantity in each grid was divided by the area (1 km

^{2}) and converted to the quantity per year.

Figure A1 shows that precipitation was high in southern Kyushu, Shikoku, the Kii Peninsula, and the Shizuoka prefecture on the Pacific coast. This is because rainfall due to typhoons or similar weather patterns during spring, summer, and autumn is quite abundant in these areas. Meanwhile, on the coast of the Sea of Japan, precipitation was high from Hokuriku to the southern part of the Tohoku region due to snowfall in winter. Precipitation in Hokkaido was generally low, especially in the northeast, which receives less than 1000 mm/yr. Evapotranspiration also changes in conjunction with the magnitude of precipitation. However, evapotranspiration is lower in the north and higher in the south, indicating that it is also affected by latitudinal temperature gradients. The surface runoff map also shows a pattern that is generally similar to that of the precipitation map, but sometimes shows clear differences (for example, between the Hokuriku and Tohoku regions on the coast of the Sea of Japan and southern Kyushu). This reflects the fact that surface runoff and infiltration differ with land use type, suggesting that underground infiltration increases in the areas where surface runoff is low. The annual means of each quantity were: 2161 mm/yr for precipitation, 753 mm/yr for evapotranspiration, 1031 mm/yr for surface runoff, and 377 mm/yr for underground infiltration.

In order to validate the results of the water balance analysis,

Figure 6 shows a correlation between the calculated flow rate,

Q_{cal}, which is the sum of surface runoff and underground infiltration, and the observed flow rate,

Q_{obs}. Here, we focused on the results from flow rate observation sites across all 109 primary water systems in Japan.

Figure 6 also shows that

Q_{cal} and

Q_{obs} are positively correlated; the slope of the linear approximation between

Q_{cal} and

Q_{obs} is 0.963, the correlation coefficient,

R^{2}, is 0.925, and the

p-value is < 0.05. These results demonstrate that the calculated flow rate,

Q_{cal}, obtained from this model is almost coincident with the observed flow rate,

Q_{obs}. It was thereby confirmed that the total outflow of the sum of surface runoff and underground infiltration in a watershed very closely approximates the annual river discharge. Therefore, this method of performing a simple water balance analysis without considering the advection between grids had a high numerical accuracy and also greatly reduced the computational load, thus proving to be a useful technique that is capable of analyzing high-resolution (1 km) grids.

#### 3.4. Calculating Japanese Plastic Emissions from Land to the Sea

We calculated the MicP numerical and mass concentrations using the population densities and urban area ratios across Japan and their approximations given in Equations (9–16). We then multiplied these values by the outflow,

Q, to estimate the numerical and mass MicP emissions for each 1 km grid cell. By summing these results nationwide, we obtained the total number and mass of the MicP particles released from the land to the sea, as shown in

Table 2.

Table 2 shows the eight calculations using approximate curves for the moving average of the observed values in addition to the approximately straight line (

y) and the maximum

(y + Δ

y/2) and minimum

(y – Δ

y/2) values at a 95% confidence interval (CI) for

C_{n} and

C_{m}.

Table 2 also defines the approximate equations used. From our results, the annual number of MicP particles emitted ranged from 0.55 to 2.54 trillion, with a median of 1.40 trillion particles. The minimum, median, and maximum values of the annual MicP emissions by mass were 65, 223, and 503 t/yr, respectively. The maximum and minimum values of both the number and mass MicP emissions corresponded to the maximum and minimum values from the linear approximation at a CI = 95%. Concerning this approximation from the raw data and from the curve of the moving average values, the number and mass MicP emissions were 1.27–1.67 trillion particles or 204–294 t/yr, respectively. The differences between these values are low, suggesting that the differences among the various approximations were also minimal.

We examined the value of MacP/MicP,

a, which is required to obtain the amount of MacP mass concentration emitted from the MicP mass concentration.

Figure 7 shows a boxplot of MicP and MacP mass concentrations and their ratio,

a, with partially corrected and organized results from Lebreton et al. [

41]. Since there were few measured data of mass concentrations of both MicP and MacP in the data of Lebreton et al. [

41], we also included data estimated from the MicP numerical concentrations. Additionally, the results for the Yangtze River in China, whose MicP and MacP concentrations were very large, as presented by Lebreton et al. [

41], were excluded, bringing

n to 29 for each case in

Figure 7. As a result, the MicP mass concentration was distributed over four orders of magnitude, from 10

^{−2} to 10

^{1}. The median and mean values were 0.53 and 5.50 mg/m

^{3}, respectively, which are generally higher than the data for rivers in Japan shown in this study (

Figure 3b). The median and mean values were 4.4 and 7.0 times larger than those in this study, respectively. However, the MacP mass concentration was greater than the MicP mass concentration and was distributed from 10

^{−1} to 10

^{1} and the median and mean MacP mass concentrations were 4.02 and 12.3 mg/m

^{3}, respectively. By considering the mass concentration ratios of MacP and MicP shown in

Figure 7b, we also found that the order of magnitude varied widely, from 10

^{−2} to 10

^{2}. In

Figure 7b, the 25%, 50% (median), and 75% quartiles were 2.28, 8.50, and 35.2, respectively, with a mean value of 20.7.

Table 3 summarizes the mass concentration ratio,

a, based on the results obtained from the study of Lebreton et al. [

41], as well as the data of Schmidt et al. [

42]. The median and mean values of the MacP and MicP mass concentrations were calculated (

Figure 7a) and their ratios are shown in

Table 3; the median and mean values of

a, shown in

Figure 7b, are also shown. It is worth noting that Schmidt et al. [

42] did not provide a list of MacP and MicP mass concentrations, but only showed their means and medians. Consequently, the mean and median MacP/MicP values are not displayed here. The range of MacP/MicP values was as wide as 0.77–20.66. The maximum value represents the mean MacP/MicP, as this value is affected by large values of 100 or more, as shown in

Figure 7b, making the MacP/MicP conceivably inappropriate as a representation of the data. Additionally, it is generally unlikely that MacP/MicP < 1, considering that most MicPs are secondary microplastics formed by the fragmentation of MacPs. Therefore, we selected four cases (2.24, 3.13, 7.66, and 8.50), excluding the minimum and maximum values in

Table 3, as the mass concentration ratios,

a, for obtaining the MacP mass concentration from that of MicP. From these four cases, we obtained eight cases for MicP, 32 cases for MacP, and their sums.

Figure 8 shows the annual values of plastic input from the land to the sea in Japan. Here, the results for MicP, MacP, and their sums are displayed as boxplots, as in

Figure 7. It should be noted that the results for MicP inputs were the same as in

Table 2. From

Figure 8, the minimum, median, and maximum values of MacP inputs are 146, 946, and 4273 t/yr, respectively. These values are larger than the MicP inputs corresponding to the MacP/MicP. Additionally, the total plastic input (MicP + MacP) was also widely distributed, in the range of 210–4776 t/yr, but the 25%, 50% (median), and 75% quartile values were 712, 1310, and 2074 t/yr, respectively. From this, it is conceivable that 1000–2000 tons of plastic are flowing out of Japan into the surrounding waters in a single year.

Plastic emissions maps of Japan are shown in

Figure 9 and show the regional emissions characteristics. A linear approximation was used for calculating the MicP mass concentrations using Equations (10) and (12), and a value of 3.13 was used as the mass concentration ratio,

a. The result in this case represents the median of 32 cases of total plastic input. From the results shown in

Figure 9, it is clear that plastic emissions were larger with higher population densities and more urbanized areas in both the Tokyo metropolitan area and in other large cities, especially Nagoya and Osaka. Moreover, the results for population density and urban area ratio exhibit similar patterns because they have similar distributions. It is noteworthy that our method allows for the mapping of plastic emissions at a very high-resolution (1 km grid). Therefore, using this method, it is also possible to calculate the plastic emissions for each river basin and each administrative district individually. As an example,

Table A2 shows the minimum, median, and maximum values of plastic emissions by prefecture across Japan.