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© The Author(s), 2018. This article is distributed under the terms of the Creative Commons Attribution License. The definitive version was published in Nonlinear Processes in Geophysics 25 (2018): 267-278, doi:10.5194/npg-25-267-2018., Trajectory encounter volume – the volume of fluid that passes close to a reference fluid parcel over some time interval – has been recently introduced as a measure of mixing potential of a flow. Diffusivity is the most commonly used characteristic of turbulent diffusion. We derive the analytical relationship between the encounter volume and diffusivity under the assumption of an isotropic random walk, i.e., diffusive motion, in one and two dimensions. We apply the derived formulas to produce maps of encounter volume and the corresponding diffusivity in the Gulf Stream region of the North Atlantic based on satellite altimetry, and discuss the mixing properties of Gulf Stream rings. Advantages offered by the derived formula for estimating diffusivity from oceanographic data are discussed, as well as applications to other disciplines., This work was supported by NSF grants OCE-1558806 and EAR-1520825, and NASA grant NNX14AH29G.

© The Author(s), 2018. This article is distributed under the terms of the Creative Commons Attribution License. The definitive version was published in Nonlinear Processes in Geophysics 25 (2018): 267-278, doi:10.5194/npg-25-267-2018., Trajectory encounter volume – the volume of fluid that passes close to a reference fluid parcel over some time interval – has been recently introduced as a measure of mixing potential of a flow. Diffusivity is the most commonly used characteristic of turbulent diffusion. We derive the analytical relationship between the encounter volume and diffusivity under the assumption of an isotropic random walk, i.e., diffusive motion, in one and two dimensions. We apply the derived formulas to produce maps of encounter volume and the corresponding diffusivity in the Gulf Stream region of the North Atlantic based on satellite altimetry, and discuss the mixing properties of Gulf Stream rings. Advantages offered by the derived formula for estimating diffusivity from oceanographic data are discussed, as well as applications to other disciplines., This work was supported by NSF grants OCE-1558806 and EAR-1520825, and NASA grant NNX14AH29G.

© The Author(s), 2013. This article is distributed under the terms of the Creative Commons Attribution License. The definitive version was published in Biogeosciences 10 (2013): 2159-2167, doi:10.5194/bg-10-2159-2013., Radium has four naturally occurring isotopes that have proven useful in constraining water mass source, age, and mixing rates in the coastal and open ocean. In this study, we used radium isotopes to determine the fate and flux of runoff-derived cesium from the Fukushima Dai-ichi Nuclear Power Plant (FNPP). During a June 2011 cruise, the highest cesium (Cs) concentrations were found along the eastern shelf of northern Japan, from Fukushima south, to the edge of the Kuroshio Current, and in an eddy ~ 130 km from the FNPP site. Locations with the highest cesium also had some of the highest radium activities, suggesting much of the direct ocean discharges of Cs remained in the coastal zone 2–3 months after the accident. We used a short-lived Ra isotope (223Ra, t1/2 = 11.4 d) to derive an average water mass age (Tr) in the coastal zone of 32 days. To ground-truth the Ra age model, we conducted a direct, station-by-station comparison of water mass ages with a numerical oceanographic model and found them to be in excellent agreement (model avg. Tr = 27 days). From these independent Tr values and the inventory of Cs within the water column at the time of our cruise, we were able to calculate an offshore 134Cs flux of 3.9–4.6 × 1013 Bq d−1. Radium-228 (t1/2 = 5.75 yr) was used to derive a vertical eddy diffusivity (Kz) of 0.7 m2 d−1 (0.1 cm2 s−1); from this Kz and 134Cs inventory, we estimated a 134Cs flux across the pycnocline of 1.8 × 104 Bq d−1 for the same time period. On average, our results show that horizontal mixing loss of Cs from the coastal zone was ~ 109 greater than vertical exchange below the surface mixed layer. Finally, a mixing/dilution model that utilized our Ra-based and oceanographic model water mass ages produced a direct ocean discharge of 134Cs from the FNPP of 11–16 PBq at the time of the peak release in early April 2011. Our results can be used to calculate discharge of other water-soluble radionuclides that were released to the ocean directly from t, The authors thank the Gordon and Betty Moore Foundation for funding this effort.

© The Author(s), 2013. This article is distributed under the terms of the Creative Commons Attribution License. The definitive version was published in Biogeosciences 10 (2013): 2159-2167, doi:10.5194/bg-10-2159-2013., Radium has four naturally occurring isotopes that have proven useful in constraining water mass source, age, and mixing rates in the coastal and open ocean. In this study, we used radium isotopes to determine the fate and flux of runoff-derived cesium from the Fukushima Dai-ichi Nuclear Power Plant (FNPP). During a June 2011 cruise, the highest cesium (Cs) concentrations were found along the eastern shelf of northern Japan, from Fukushima south, to the edge of the Kuroshio Current, and in an eddy ~ 130 km from the FNPP site. Locations with the highest cesium also had some of the highest radium activities, suggesting much of the direct ocean discharges of Cs remained in the coastal zone 2–3 months after the accident. We used a short-lived Ra isotope (223Ra, t1/2 = 11.4 d) to derive an average water mass age (Tr) in the coastal zone of 32 days. To ground-truth the Ra age model, we conducted a direct, station-by-station comparison of water mass ages with a numerical oceanographic model and found them to be in excellent agreement (model avg. Tr = 27 days). From these independent Tr values and the inventory of Cs within the water column at the time of our cruise, we were able to calculate an offshore 134Cs flux of 3.9–4.6 × 1013 Bq d−1. Radium-228 (t1/2 = 5.75 yr) was used to derive a vertical eddy diffusivity (Kz) of 0.7 m2 d−1 (0.1 cm2 s−1); from this Kz and 134Cs inventory, we estimated a 134Cs flux across the pycnocline of 1.8 × 104 Bq d−1 for the same time period. On average, our results show that horizontal mixing loss of Cs from the coastal zone was ~ 109 greater than vertical exchange below the surface mixed layer. Finally, a mixing/dilution model that utilized our Ra-based and oceanographic model water mass ages produced a direct ocean discharge of 134Cs from the FNPP of 11–16 PBq at the time of the peak release in early April 2011. Our results can be used to calculate discharge of other water-soluble radionuclides that were released to the ocean directly from t, The authors thank the Gordon and Betty Moore Foundation for funding this effort.

© The Author(s), 2013. This article is distributed under the terms of the Creative Commons Attribution License. The definitive version was published in Biogeosciences 10 (2013): 4973-4990, doi:10.5194/bg-10-4973-2013., The Great East Japan Earthquake and tsunami that caused a loss of power at the Fukushima nuclear power plants (FNPP) resulted in emission of radioactive isotopes into the atmosphere and the ocean. In June of 2011, an international survey measuring a variety of radionuclide isotopes, including 137Cs, was conducted in surface and subsurface waters off Japan. This paper presents the results of numerical simulations specifically aimed at interpreting these observations and investigating the spread of Fukushima-derived radionuclides off the coast of Japan and into the greater Pacific Ocean. Together, the simulations and observations allow us to study the dominant mechanisms governing this process, and to estimate the total amount of radionuclides in discharged coolant waters and atmospheric airborne radionuclide fallout. The numerical simulations are based on two different ocean circulation models, one inferred from AVISO altimetry and NCEP/NCAR reanalysis wind stress, and the second generated numerically by the NCOM model. Our simulations determine that > 95% of 137Cs remaining in the water within ~600 km of Fukushima, Japan in mid-June 2011 was due to the direct oceanic discharge. The estimated strength of the oceanic source is 16.2 ± 1.6 PBq, based on minimizing the model-data mismatch. We cannot make an accurate estimate for the atmospheric source strength since most of the fallout cesium had left the survey area by mid-June. The model explained several key features of the observed 137Cs distribution. First, the absence of 137Cs at the southernmost stations is attributed to the Kuroshio Current acting as a transport barrier against the southward progression of 137Cs. Second, the largest 137Cs concentrations were associated with a semi-permanent eddy that entrained 137Cs-rich waters, collecting and stirring them around the eddy perimeter. Finally, the intermediate 137Cs concentrations at the westernmost stations are attributed to younger, and therefore less Cs-rich, c, Irina Rypina was partially supported by Grant NSF-OCE-0725796. This work is funded by the Gordon and Betty Moore Foundation through Grant GBMF3007 to Ken Buesseler.

© The Author(s), 2013. This article is distributed under the terms of the Creative Commons Attribution License. The definitive version was published in Biogeosciences 10 (2013): 2159-2167, doi:10.5194/bg-10-2159-2013., Radium has four naturally occurring isotopes that have proven useful in constraining water mass source, age, and mixing rates in the coastal and open ocean. In this study, we used radium isotopes to determine the fate and flux of runoff-derived cesium from the Fukushima Dai-ichi Nuclear Power Plant (FNPP). During a June 2011 cruise, the highest cesium (Cs) concentrations were found along the eastern shelf of northern Japan, from Fukushima south, to the edge of the Kuroshio Current, and in an eddy ~ 130 km from the FNPP site. Locations with the highest cesium also had some of the highest radium activities, suggesting much of the direct ocean discharges of Cs remained in the coastal zone 2–3 months after the accident. We used a short-lived Ra isotope (223Ra, t1/2 = 11.4 d) to derive an average water mass age (Tr) in the coastal zone of 32 days. To ground-truth the Ra age model, we conducted a direct, station-by-station comparison of water mass ages with a numerical oceanographic model and found them to be in excellent agreement (model avg. Tr = 27 days). From these independent Tr values and the inventory of Cs within the water column at the time of our cruise, we were able to calculate an offshore 134Cs flux of 3.9–4.6 × 1013 Bq d−1. Radium-228 (t1/2 = 5.75 yr) was used to derive a vertical eddy diffusivity (Kz) of 0.7 m2 d−1 (0.1 cm2 s−1); from this Kz and 134Cs inventory, we estimated a 134Cs flux across the pycnocline of 1.8 × 104 Bq d−1 for the same time period. On average, our results show that horizontal mixing loss of Cs from the coastal zone was ~ 109 greater than vertical exchange below the surface mixed layer. Finally, a mixing/dilution model that utilized our Ra-based and oceanographic model water mass ages produced a direct ocean discharge of 134Cs from the FNPP of 11–16 PBq at the time of the peak release in early April 2011. Our results can be used to calculate discharge of other water-soluble radionuclides that were released to the ocean directly from t, The authors thank the Gordon and Betty Moore Foundation for funding this effort.

© The Author(s), 2013. This article is distributed under the terms of the Creative Commons Attribution License. The definitive version was published in Biogeosciences 10 (2013): 4973-4990, doi:10.5194/bg-10-4973-2013., The Great East Japan Earthquake and tsunami that caused a loss of power at the Fukushima nuclear power plants (FNPP) resulted in emission of radioactive isotopes into the atmosphere and the ocean. In June of 2011, an international survey measuring a variety of radionuclide isotopes, including 137Cs, was conducted in surface and subsurface waters off Japan. This paper presents the results of numerical simulations specifically aimed at interpreting these observations and investigating the spread of Fukushima-derived radionuclides off the coast of Japan and into the greater Pacific Ocean. Together, the simulations and observations allow us to study the dominant mechanisms governing this process, and to estimate the total amount of radionuclides in discharged coolant waters and atmospheric airborne radionuclide fallout. The numerical simulations are based on two different ocean circulation models, one inferred from AVISO altimetry and NCEP/NCAR reanalysis wind stress, and the second generated numerically by the NCOM model. Our simulations determine that > 95% of 137Cs remaining in the water within ~600 km of Fukushima, Japan in mid-June 2011 was due to the direct oceanic discharge. The estimated strength of the oceanic source is 16.2 ± 1.6 PBq, based on minimizing the model-data mismatch. We cannot make an accurate estimate for the atmospheric source strength since most of the fallout cesium had left the survey area by mid-June. The model explained several key features of the observed 137Cs distribution. First, the absence of 137Cs at the southernmost stations is attributed to the Kuroshio Current acting as a transport barrier against the southward progression of 137Cs. Second, the largest 137Cs concentrations were associated with a semi-permanent eddy that entrained 137Cs-rich waters, collecting and stirring them around the eddy perimeter. Finally, the intermediate 137Cs concentrations at the westernmost stations are attributed to younger, and therefore less Cs-rich, c, Irina Rypina was partially supported by Grant NSF-OCE-0725796. This work is funded by the Gordon and Betty Moore Foundation through Grant GBMF3007 to Ken Buesseler.

© The Author(s), 2013. This article is distributed under the terms of the Creative Commons Attribution License. The definitive version was published in Biogeosciences 10 (2013): 4973-4990, doi:10.5194/bg-10-4973-2013., The Great East Japan Earthquake and tsunami that caused a loss of power at the Fukushima nuclear power plants (FNPP) resulted in emission of radioactive isotopes into the atmosphere and the ocean. In June of 2011, an international survey measuring a variety of radionuclide isotopes, including 137Cs, was conducted in surface and subsurface waters off Japan. This paper presents the results of numerical simulations specifically aimed at interpreting these observations and investigating the spread of Fukushima-derived radionuclides off the coast of Japan and into the greater Pacific Ocean. Together, the simulations and observations allow us to study the dominant mechanisms governing this process, and to estimate the total amount of radionuclides in discharged coolant waters and atmospheric airborne radionuclide fallout. The numerical simulations are based on two different ocean circulation models, one inferred from AVISO altimetry and NCEP/NCAR reanalysis wind stress, and the second generated numerically by the NCOM model. Our simulations determine that > 95% of 137Cs remaining in the water within ~600 km of Fukushima, Japan in mid-June 2011 was due to the direct oceanic discharge. The estimated strength of the oceanic source is 16.2 ± 1.6 PBq, based on minimizing the model-data mismatch. We cannot make an accurate estimate for the atmospheric source strength since most of the fallout cesium had left the survey area by mid-June. The model explained several key features of the observed 137Cs distribution. First, the absence of 137Cs at the southernmost stations is attributed to the Kuroshio Current acting as a transport barrier against the southward progression of 137Cs. Second, the largest 137Cs concentrations were associated with a semi-permanent eddy that entrained 137Cs-rich waters, collecting and stirring them around the eddy perimeter. Finally, the intermediate 137Cs concentrations at the westernmost stations are attributed to younger, and therefore less Cs-rich, c, Irina Rypina was partially supported by Grant NSF-OCE-0725796. This work is funded by the Gordon and Betty Moore Foundation through Grant GBMF3007 to Ken Buesseler.