Of the 24,954 trajectories that interacted with the mixed layer in 2011, the percentage of interactions in each 0.25° grid cell is shown in Figure 3 (color contours). The highest probabilities (≥2.5%) for mixed layer interaction can be seen in the immediate vicinity of the Japan coast, to the east of the FDNPP (yellow contours). These regions of mixed layer interaction overlap the Stohl et al. ( 2012 ) model‐based estimate of the location of maximum atmospheric deposition (Figure 3 purple polygon and subpanel). This reassuring result confirms that the observed Cs F likely originated from the vicinity of FDNPP in 2011. The model also suggests that the timing of the Fukushima accident (when mixed layers were deep and mode waters were being formed) was crucial to the 26.5σ θ isopycnal's exposure to radionuclides ( Movie S1 and Figure S3 ). During 2011, this exposure occurred within the purple polygon region most often between 19 and 26 March 2011 (Figure S4 ). Note that the purple polygon and the areas with the highest probability of mixed layer interaction overlap with the L‐CMW, D‐CMW, and TRMW formation regions (Figure 1 ), and the 26.5σ θ isopycnal lies within the density range of both the denser water masses, D‐CMW and TRMW. Furthermore, the presence of high‐interaction areas (Figure 3 , yellow contours) within the polygon suggests that these denser water masses may have been forming as far south as ~36°N during the spring of 2011 (Figure S3 , orange crosses). According to HYCOM, in the days following the March accident in 2011, the densest value attained by the mixed layer within the polygon ranged between 23.3 and 26.8σ θ but it was the denser waters in the range of 26.2–26.6σ θ that were amongst the most common (Figure S5 ).

All particle backward trajectories (light gray) overlaid with random selection of trajectories (dark gray) as examples of trajectory behavior. Colored contours indicate the probability of a trajectory interacting with the mixed layer between 15 March 2011 and 31 December 2011. Highest probability is 4.5%, and color bar is saturated at 2.5%. Theis outlined in pink. Red star indicates FDNPP location. Upper‐right subplot is a model estimate of atmospheric deposition coverage and concentration adapted from Stohl et al. (); color scale blue (>0) to yellow (0.025 PBq). Purple polygon roughly outlines Stohl et al.'s estimate of concentration greater than 0.02 PBq (dark orange to yellow). FDNPP = Fukushima Daiichi Nuclear Power Plant.

The backward trajectory paths were spread across a broad swath of the northwestern Pacific (Figure 3 , light gray), suggesting a large range of possible pathways that could bring water parcels to the observed location via modeled oceanic currents on the 26.5σ θ isopycnal. FDNPP radionuclides were introduced at the surface in 2011; therefore, we focus on when and where the 26.5σ θ isopycnal interacted with (i.e., lay within) the mixed layer during that year, assuming that this is how Cs F was introduced to this isopycnal. The mixed layer was estimated using the 0.03 kg m −3 difference criterion (de Boyer Montégut et al., 2004 ; Dong et al., 2008 ; Holte et al., 2017 ). All trajectories passing within ±3 days and ± 0.25° latitude and longitude of each interaction time/location were considered to have interacted with the mixed layer.

4.2 Probability and Arrival Date Maps

Of the 300,000+ particles released from the pink box (Figure 3), 6,772 (or 2.2%) trajectories interacted with the mixed layer inside the region of maximum atmospheric deposition (purple polygon in Figure 3) in 2011. Henceforth, these trajectories are referred to as successful. The statistical techniques of probability and arrival date mapping (Rypina, Jayne, et al., 2014; Rypina, Llopiz, et al., 2014; Rypina et al., 2016, 2019) were applied to the successful trajectories, to better understand the timing and pathways of the particles most likely to transport the Cs F signal. Note, however, that even though trajectories were simulated backward in time from the pink release box, we now discuss the movement of these fluid parcels forward in time from when they exited the purple polygon in 2011 to when they arrived in the release box.

The probability map (Figure 4b) represents the percentage of successful trajectories that visit different geographical locations throughout the study region. Probabilities were computed by gridding the domain into 0.25° × 0.25° bins, summing the number of successful trajectories that passed through each bin and dividing by the total number of successful trajectories. The 2‐year timescale for the trip is illustrated in the arrival date map (Figure 4a), which shows the average first arrival of all successful trajectories to each bin.

Figure 4 Open in figure viewer PowerPoint 2006 Maps representing the average arrival date at each 0.25° grid cell (a, c, e) and the percentage probability for trajectories to pass through each grid cell (b, d, f) for the different simulations: (a, b) successful backward trajectories, (c, d) forward trajectories, and (e, f) forward trajectories released north of 39°N. Green curves represent by way of example a single instance of the north wall of the KE (solid) based on a snapshot of sea surface height and temperature and an estimate of the climatological core of the current (dashed) based on hydrography (Isoguchi et al.,, interpretation of their Figures 3 and 2 a, respectively). Symbols are the same as in Figure 3

The red colors in the probability map (Figure 4b) indicate the highest probability (~10% or more) and outline the most likely route for the water parcels associated with successful trajectories to travel from the purple polygon in 2011 to the observed location in 2013. This route runs eastward from Japan and extends along the path of the KE out into the western Pacific. The abrupt transition from red to yellow/green south of the KE between the coast and ~145°E indicates that on 26.5σ θ only a few successful trajectories crossed the KE within this longitudinal band to enter the recirculation region to the south, where NPSTMW is formed and where the subsurface Cs F was found in 2012 in lighter waters (Aoyama et al., 2016; Kumamoto et al., 2014). Trajectories entering the recirculation region most likely crossed the KE to the east of 145°E and before recirculating anticyclonically. The arrival date map (Figure 4a) shows an associated abrupt transition from early arrival dates (dark blue) inside this fast‐flowing segment of the KE as it first moves offshore to significantly later arrival dates (cyan/blue) just to the south. Both maps suggest limited entry to the recirculation region west of 145°E. Further east, the red/orange high‐probability path widens and diffuses as the KE becomes less coherent. However, the highest probability path (brightest red) still lies along the track and to the north of the KE out to ~165–167°E, where the high‐probability path turns sharply south, crossing the KE to arrive in the pink box. The probability that trajectories will cross the KE and head south toward the location of the 2013 observations is nearly 25% at 165°E, whereas near the recirculation, the probability is 1% or less (yellow/green colors). This result suggests that where the current is strongest, the KE is acting as a barrier to southward particle transport at the depth of the 26.5σ θ surface, at least for those trajectories that eventually arrive at the 30°N, 166°E observation location in 2013.