Measuring bismuth‐210, its parent, and daughter in aquatic systems

210Bi (t1/2: 5.01 d)—the daughter of 210Pb and parent of 210Po—has rarely been measured in aquatic systems, and its behavior in the water column is poorly understood. In this article, I present a method for quickly measuring 210Pb, 210Bi, and 210Po in aquatic samples, where (1) 210Bi and 210Po are scavenged onto an anion solid‐phase extraction disk within 15 min of pretreating the sample; (2) beta decay of 210Bi is counted on the disk immediately thereafter; (3) 210Po is subsequently removed from the disk and redeposited on a copper plate for α‐spectroscopy; and (4) 210Pb is determined via the ingrowth of 210Bi. I present decay‐corrected calculations for total, dissolved, and particle‐bound fractions of each nuclide and conclude with an analysis of 210Pb, 210Bi, and 210Po activities in rain, dreissenid (quagga) mussels, and water samples from the Milwaukee Inner Harbor in Lake Michigan. Results show that the loss of lead on the anion solid‐phase extraction disks was negligible (0.2% ± 2.1%; ± 1 SD, n = 4), and the sorption of bismuth was complete (99% ± 2%; ± 1 SD, n = 16). Relative mean absolute deviations of duplicate sample analyses of lake water were 2.4% ± 1.9% for 210Pb (geometric mean of total sample activity: 3.0 disintegrations per minute [dpm], n = 6), 7.7% ± 5.8% for 210Bi (geometric mean of total sample activity: 2.6 dpm, n = 8), and 2.7% ± 1.7% for 210Po (geometric mean of total sample activity: 1.4 dpm, n = 8).

Over the past 50 years, the naturally occurring radionuclide of lead-210 ( 210 Pb t 1/2 : 22.3 years) and its granddaughter polonium-210 ( 210 Po t 1/2 : 138.4 d) have been measured and used as a tracer of particle flux in the water column (e.g., Shannon et al. 1970;Bacon et al. 1976;Rutgers van der Loeff and Geibert 2008;Verdeny et al. 2009). Over that same timeframe, the daughter of 210 Pb, Bi t 1/2 : 5.01 d), has rarely been measured and its behavior in the water column is poorly understood. Fowler et al. (2010) encouraged the radiotracer community to measure 210 Bi in aquatic systems based on bismuth's apparent affinity for biogenic particles and suggested that the 210 Bi/ 210 Pb nuclide pair could serve as a useful tracer for short-term scavenging processes in the upper water column. Wang et al. (2019) and Kim and Hong (2019) have recently repeated this call. The primary advantage of a short-lived radionuclide tracer is its ability to rapidly respond to any change in scavenging flux, with the 210 Bi/ 210 Pb tracer capable of reaching a new steady-state disequilibrium as much as 30 times faster than the 210 Po/ 210 Pb pair. If radionuclide profiles are mistakenly assumed to be at steady-state, tracer-derived particle fluxes can greatly underestimate or exceed true flux conditions.
Interest in measuring 210 Bi waxed and waned from the early-1990s to the early-2000s (e.g., Church et al. 1994;Tokieda et al. 1994;Marley et al. 1999;Katzlberger et al. 2001;Biggin et al. 2002). Unfortunately, none of these techniques have been exploited, and the application of 210 Bi as a tracer of aquatic scavenging processes has still not been explored. To date, only a few estimates of in situ 210 Bi activity exist, from the thermal springs in Bad Gastein (Austria) (Katzlberger et al. 2001), and the waters of Funka Bay (Tokieda et al. 1994) and the Irish Sea (Biggin et al. 2002).
The methods referenced above all have their strengths. Procedures for separating 210 Bi make use of precipitation, solvent extraction, ion exchange chromatography, and electrochemical techniques (Marley et al. 1999, and references therein). However, we have found-from our work with the short-lived nuclide yttrium-90 ( 90 Y t 1/2 : 2.67 d; Waples and Orlandini 2010)-that time is of essence due to the rapid decay of the analyte. With respect to 210 Pb,210 Bi, and 210 Po, the analyses of 210 Pb and 210 Po activity are secondary to the speed and ease with which 210 Bi can be isolated and counted. Given this criterion, the method of Marley et al. (1999) stands out. Marley et al. (1999) used an anion solid-phase extraction (SPE) disk to separate the 210 Bi and 210 Po progeny from their 210 Pb parent with less than 1% interference, where the anionic chloride complexes of bismuth and polonium have affinities *Correspondence: jwaples@uwm.edu This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited.
(K d > 10 4 ) for the disk's anionic chelating particles that greatly exceed those of lead (K d~1 0). Because the disk itself was then counted directly on an alpha/beta gas-flow proportional counter, both the separation and initial measurement of 210 Bi were quickly achieved. However, Marley et al. (1999) also counted 210 Po on the SPE disk with the proportional counter, and here the method is problematic. While Marley et al. (1999) advocated their method for measuring 210 Pb,210 Bi, and 210 Po in aquatic samples, they only applied their technique to rain and snow, where natural activities were high and the whole sample could be eluted through the disk. In large samples with low natural activities, the total or dissolved fraction activities of 210 Pb,210 Bi,and 210 Po must be concentrated by scavenging. Unknown and variable scavenging efficiencies require that an isotope of the target nuclide must also be added as a yield monitor. Because both 210 Po and its yield monitor 209 Po decay by alpha particle emission, α-spectroscopy is required to resolve and quantify the activity of each isotope, and this cannot be done while polonium is still strongly sorbed to the SPE disk.
In this study, I modify the method of Marley et al. (1999) slightly, so that polonium is removed from the SPE disk and redeposited on a copper plate for α-spectroscopy. I also expand on procedural topics that were either not discussed or only briefly developed, including sample pretreatment, anion SPE disk sorption efficiencies, detector efficiencies and backgrounds, and decay-corrected calculations for total, dissolved, and particle-bound fractions of 210 Pb,210 Bi,and 210 Po. I conclude with an analysis of 210 Pb,210 Bi,and 210 Po activities in rain, dreissenid (quagga) mussels, and water samples from the Milwaukee Inner Harbor in Lake Michigan, where the emphasis here is placed on method assessment and precision, and comparison with reported activities in the literature. An additional manuscript describing a larger environmental data set of 210 Pb,210 Bi,and 210 Po activities-including the values presented here-and an analysis of their scavenging in the water column is in preparation (J. T. Waples unpubl.).

Materials and procedures
Measuring 210 Pb,210 Bi,and 210 Po in a water sample My approach to measuring both dissolved and particlebound fractions of 210 Pb,210 Bi,and 210 Po in a water sample is shown in a schematic in Fig. 1 and a more detailed timeline in Fig. 2. The description of this method is organized with the timeline. After sample pretreatment (where both particlebound and dissolved nuclide fractions that have been scavenged on a ferric hydroxide precipitate are filtered and digested in nitric acid), the approach, in brief, calls for the immediate and complete separation of bismuth and polonium from lead on an anion SPE disk and counting the disk-first for 210 Bi via β-decay, then for 207 Bi via γ-emission to determine yield. Polonium is then removed from the SPE disk, plated to copper, and α-counted for 210 Po and the yield monitor 209 Po. Total and particle-bound 210 Pb fractions are held for approximately 1 month and finally measured via 210 Bi that has grown into secular equilibrium with its parent.

Sample collection (t 0 )
The volume of water required to measure the activity of any radionuclide in both dissolved and particle-bound fractions will depend on many factors. These include the activity of the nuclide, the nuclide's affinity for particle sorption, the Fig. 1. A schematic of separation procedures for the determination of 210 Pb,210 Bi, and 210 Po.
half-life of the nuclide and the speed at which the sample can be processed, and the degree of accuracy required by any specific application of the nuclide as a tracer (Waples and Orlandini 2010). Based on previous measurements of 210 Pb in Lake Superior (Chai and Urban 2004) and the Clinton River in southeastern Michigan (Mudbidre et al. 2014), an initial estimate of~50 L of water was considered adequate for the analysis of both dissolved and particle-bound fractions of 210 Pb,210 Bi,and 210 Po in Lake Michigan.
Water samples were collected with a submersible pump and stored in large plastic barrels. At least one~50 L water sample (S1) was collected for the immediate analysis of dissolved and particle-bound fractions of 210 Bi and 210 Po and the subsequent analysis of particle-bound 210 Pb. At least one additional~50 L water sample (S2) was collected for the eventual analysis of total (dissolved + particle-bound) 210 Pb. Time of sample collection was noted as t 0 .
The S2 sample was immediately weighed, acidified with 500 mL of concentrated HCl (12 M), spiked with a calibrated yield monitor of 207 Bi (e.g., 0.6 Bq), and stored for later analysis. S1 sample processing (t 1 ) The S1 sample was weighed, then quickly filtered (< 2 h after sample collection) through a nitrocellulose membrane (0.45 μm, 293 mm, Millipore) to separate the operationally defined particulate fraction from the dissolved fraction. The sample filtrate was collected in a large (~75-L) plastic beaker. The time of filtration was noted (t 1a ) and the empty sample container was weighed again to determine sample volume. The filter containing the particulate nuclide fraction was placed in a 500-mL beaker, spiked with calibrated yield monitors of 207 Bi (e.g., 0.6 Bq) and 209 Po (e.g., 0.1 Bq), and set aside for digestion and subsequent analysis.
The S1 sample filtrate was then acidified with 500 mL of concentrated HCl (12 M) and spiked with calibrated yield monitors of 207 Bi (e.g., 0.6 Bq) and 209 Po (e.g., 0.1 Bq). The solution was stirred for 15 min, after which 1 mg L −1 ferrous iron was added (i.e., 50 mg Fe +2 in 50 L water) as ferrous sulfate (Waples and Orlandini 2010). After stirring for several additional minutes, 500 mL of concentrated NH 4 OH (14 M) was added to form a precipitate of ferric hydroxide. This precipitate-carrying the sorbed dissolved nuclide fractions of 210 Pb,210 Bi, and 210 Po-was collected onto another nitrocellulose filter (0.45 μm, 293 mm, Millipore) and saved, with the time of filtration noted as t 1b .
The nitrocellulose filters carrying both dissolved and particle-bound sample fractions were dissolved by adding 20 mL of concentrated HNO 3 (16 M) to each sample beaker. The beakers were covered with a watch glass and heated gently for~1 h. The watch glasses were then removed, and the samples were evaporated to near dryness at temperatures not exceeding~100 C (to minimize the volatilization of polonium). The samples were then removed from heat and, once dry, reconstituted with 50 mL of 0.5 M HCl.
To remove any remaining particulate mineral matter, both dissolved and particle-bound sample fractions were again filtered through nitrocellulose filters (0.45 μm, 47 mm, Whatman) secured in a 47-mm filtration apparatus (Nalgene). Each filter was rinsed three times with~10 mL of 0.5 M HCl, and the filters were discarded. Fig. 2. A timeline of separation procedures for the determination of total, particle-bound, and dissolved fractions of 210 Pb,210 Bi, and 210 Po.

Nuclide separation on anion SPE membrane disks (t 2 )
Empore™ anion SPE membrane disks (3 M, 47 mm, product number 2252, now manufactured by CDS Analytical) were placed in a Nalgene filter apparatus with a 250-mL receiver. Vacuum (~400 mbar) was applied using a water aspirator. The filters were wetted with~10 mL of ethanol and then rinsed three times with 10 mL of 0.5 M HCl. The filter apparatus receiver was emptied and cleaned with distilled water before loading the S1 sample fractions onto the anion SPE disks. Sample elution times were generally less than 5 min. The time of elution was noted as t 2a for the S1 particle-bound fraction and t 2b for the S1 dissolved fraction.
Each anion SPE disk was again rinsed three times with 10 mL of 0.5 M HCl. Bismuth and polonium isotopes from both sample fractions were now sorbed to the disks. The eluate from the S1 particle-bound fraction was carefully transferred to a clean beaker, spiked with 207 Bi (e.g., 0.6 Bq), and covered for later analysis of particle-bound 210 Pb (via the ingrowth of 210 Bi). The eluate from the S1 dissolved fraction was generally discarded. However, this eluate can be used to determine the dissolved 210 Pb fraction if a lead yield monitor is added to the original sample (see "Comments and recommendations" section).
To prepare the anion SPE disks for β-counting, the filters were again placed under vacuum and rinsed three times with 10 mL of distilled water. The disks were then transferred to covered beakers and exposed to vapors of 50% NH 4 OH for 5 min, which effectively neutralized any residual acid (Marley et al. 1999). Finally, the disks were placed onto cupped stainless steel planchets (2-in. diameter, available from A. F. Murphy Die & Machine) and allowed to air-dry for~30 min.
β-Counting 210 Bi decay on the anion SPE membrane disk (t 3 ) The dried anion SPE disks in cupped stainless steel planchets were placed in a low background gas-flow proportional counter with eight 2.25-in.-diameter detectors and anticoincidence circuitry (G542 System, Gamma Products) and counted over a series of four sessions spanning a~30-d period (e.g., at 0, 5, 10, and 25 d after sample preparation). Each counting session consisted of a series of 10, 150-min counting intervals. The time of each counting interval (t 3 ) was recorded.

γ-Counting 207 Bi recovery on the anion SPE membrane disk (t 4 )
The anion SPE disks in planchets were then put in plastic Petri dishes and placed (face down) in an HPGe planar detector (models GMX-23210-P and LO-AX-70450/30-S, Ortec). Gamma counts were measured over an average period of 2 × 10 5 s. 207 Bi recovery was determined by peak analysis in the 570 keV region. Gamma spectrum analysis was performed using Maestro software (v. 6.04, Advanced Measurement Technology). Peak analyses reported net peak areas and net area uncertainty (AE 1 SD). The time of the count (t 4 ) was noted.

Removal of Po isotopes from the anion SPE membrane disk (t 5 )
After βand γ-counting, the anion SPE disks were again mounted in a 47-mm filtration apparatus (Nalgene), placed under vacuum, and rewetted with~10 mL of ethanol. The disks were then carefully rinsed four times with a total of 40 mL of distilled water and the filter apparatus receiver was emptied and cleaned with distilled water.
After the anion SPE disks had been wetted and rinsed-and "the ethanol in the filter apparatus receiver removed"-the disks were placed under vacuum and rinsed with 80 mL of 8 M HNO 3 to elute the polonium isotopes of 210 Po and 209 Po. I emphasize the importance of removing all ethanol from the eluate sample because "ethanol and nitric acid will react violently when heated." The eluate of nitric acid and polonium isotopes was then transferred from the filter apparatus receiver to a 500-mL beaker and evaporated to near dryness on a hotplate, with the sample temperature not exceeding~100 C.

Plating Po isotopes on a copper disk (t 6 )
The polonium isotopes of 210 Po and 209 Po were spontaneously deposited on a copper disk using a modified methodology of Robbins and Edgington (1975), MacKenzie and Scott (1979), and Kostenko (1982). Briefly, the dried polonium sample was first reconstituted with 50 mL of 0.1 M HCl. Next, 0.1 g of L-ascorbic acid (Sigma Aldrich) was added to the beaker to prevent any iron in the sample from interfering with the plating of polonium. The pH of the solution was adjusted to~1 with 6 M HCl and the entire contents of the beaker was transferred to a 125-mL Nalgene wide-mouth plastic bottle. A flat copper disk (7/8-in. diameter, available from A. F. Murphy Die & Machine), which was polished on one side and sealed with a thin layer of polyurethane on the other, was added to each sample bottle (polished side up) and the bottles were capped tight, put in an oven, and heated to 95 C for~12 h (i.e., overnight). After heating, the copper disks were retrieved, rinsed with distilled water and ethanol, and allowed to dry.

α-Counting 210 Po and 209 Po on a copper disk (t 7 )
The dried copper disks were then placed in an alpha counter (Octete Plus alpha spectrometry workstation with Ultra-AS detectors, Ortec). Alpha counts were measured over a period of 1.8 × 10 5 s. 210 Po and 209 Po activities were determined by peak analyses of the 5.31 and 4.88 MeV regions, respectively. Alpha spectrum analysis was performed using Maestro software (v. 6.06, Advanced Measurement Technology). The time of the count was noted as t 7 .
Specifically, the S2 water sample was processed using the same procedure described in the t 1 "S1 sample processing (t 1 )" section above, except that both dissolved and particle-bound fractions of 210 Bi were collected onto one nitrocellulose filter to determine total 210 Pb. Because the sample was already acidified and spiked with 207 Bi, the procedure started with the addition of ferrous iron. The time of filtration was noted as t 8 .
The separation of bismuth isotopes from the total and particle-bound 210 Pb sample fractions on anion SPE disks proceeded as described in time step t 2 , except that eluates from both sample fractions were discarded. The time of elution was noted as t 9a for the S2 total 210 Pb sample and t 9b for the S1 particle-bound 210 Pb fraction.
Beta (t 10 ) and gamma (t 11 ) counting the activities of 210 Bi and 207 Bi proceeded as described in time steps t 3 and t 4 .

Yield monitors and standards
Standards of  A secondary standard of 210 Pb,210 Bi, and 210 Po (in secular equilibrium) was made by digesting~10 g of Lake Michigan sediment (collected in 1994) in 50 mL of concentrated HNO 3 . The mixture was covered and heated gently overnight and allowed to dry the following morning. The dried sediment was then reconstituted with 50 mL of 0.5 M HCl and allowed to sit for an additional day before removing the sediment by filtration through a nitrocellulose filter (0.45 μm, 47 mm, Whatman). Calibration of the sediment standard eluate was eventually achieved via 210 Po, using weighed aliquots of the NIST-calibrated 209 Po standard.

Bismuth
The sorption efficiency of bismuth on the anion SPE disks was determined by the recovery of 207 Bi on rain, mussel tissue, and particle-bound water fraction samples, where the transfer of 207 Bi to the SPE disks was complete (i.e., lossless). Procedural details are described in the "Assessment: Materials and procedures" section below.

Lead
The sorption efficiency of lead on the anion SPE disks was determined by digesting four samples of~0.5 g of Lake Michigan sediment (collected in 1994) in 20 mL of concentrated (16 M) HNO 3 . Each sample was spiked with measured volumes of the NIST-calibrated 207 Bi and 209 Po standards. The samples were heated until dry, reconstituted in 20 mL 0.5 M HCl, and stirred before removing the sediment by filtration through a nitrocellulose filter. The four samples were then run through four separate anion SPE disks and the disks were beta counted repeatedly to determine the initial 210 Bi activity in counts per minute (cpm) in the extracted sediment digestion.
The eluate from the four samples (containing any 210 Pb that passed through the SPE disks) was spiked again with the same volumes of 207 Bi and 209 Po standards and covered. After 57 d-and the complete ingrowth of 210 Bi to secular equilibrium with its parent-the four samples were again run through separate SPE disks and beta counted to determine the 210 Bi activity (cpm) in the eluate.
Because the SPE disks for each sample were beta counted on the same detector, and the transfer of lead from the eluant of the first SPE disk to the second SPE disk was complete, any decrease in 210 Bi activity on the second SPE disk could be attributed to the sorption of 210 Pb on the first SPE disk.
Detector efficiencies and backgrounds 210 Bi beta efficiency A two-standard, eight-point calibration curve was used to determine the 210 Bi beta counting efficiency of the low background gas-flow proportional counter.
Four samples containing measured masses of the sedimentderived standard, 207 Bi, and 209 Po were run through four anion SPE disks. The four disks were repeatedly counted in all eight beta detectors over a period of several weeks to determine initial (t 2 ) 210 Bi activities in cpm. The four disks were then placed in gamma counters to determine activities of the added 207 Bi and the filter extraction efficiency of bismuth. Next, the polonium isotopes were carefully extracted from each disk using 8 M nitric acid. 210 Po and 209 Po were spontaneously plated on copper disks and alpha counted to determine 210 Po activity in disintegrations per minute (dpm; where 60 dpm = 1 Bq) per gram of sediment-derived standard.
To check the calibration of the sediment-derived "house standard," and the validity of my alpha counting procedure, another calibration curve was measured using the NISTcalibrated 210 Pb standard from Eckert & Ziegler Isotope Products. Four samples containing measured masses of the calibrated 210 Pb standard and 207 Bi were run through four anion SPE disks and the four disks were then repeatedly counted in four of the eight detectors over a period of several weeks. Again, the decay of beta activity over time was used to calculate the initial (t 2 ) 210 Bi activity on the disks (cpm). The four disks were then placed in gamma counters to determine activities of the added 207 Bi.

207
Bi gamma efficiency To determine the efficiency of our gamma detectors at measuring 207 Bi, two samples were prepared using the NIST-calibrated 207 Bi standard. The anion SPE disks were first placed in cupped stainless steel planchets and wetted with ethanol. Weighed aliquots of 207 Bi standard were then spread evenly across the disks. The disks were dried on low heat, placed in plastic petri dishes, and counted face down using the same geometry employed for other standard or environmental samples.
Counts in the region of 569.7 keV were measured over an average interval of 16 d to determine the detector response to 207 Bi, where the efficiency of the response is expressed in units of cpm dpm −1 . Gamma spectrum analysis was performed using Maestro software (v. 6.04, Advanced Measurement Technology). Peak analyses reported net peak areas and net area uncertainty (AE 1 SD).

Alpha-detector background
Alpha-detector backgrounds for 210 Po and 209 Po activities in the regions of 5.31 MeV (for 210 Po) and 4.88 MeV (for 209 Po) were determined by counting blank polished copper disks for 5 × 10 5 s.

Radionuclide activity calculations
Radionuclide activities at the time of sample collection (t 0 ) were first calculated for 210 Pb, followed by 210 Bi, and finally 210 Po because activities of 210 Pb and 210 Bi were needed to make small corrections in the t 0 activities of 210 Bi and 210 Po, respectively. 210 Pb total activity Because 210 Pb activities were calculated via the ingrowth of 210 Bi, the first step to determining the total 210 Pb activity involved calculating the 210 Bi activity on the anion SPE disk 3 at time t 9a . This was done by repeatedly beta counting the SPE disk over a significant fraction of the sample's 210 Bi lifetime. The time series of 150-min measurements of gross beta activity (cpm) were then plotted as a function of e −λ Bi t , where λ Bi is the decay constant for 210 Bi (0.13835 d −1 ) and t is the time elapsed between the start of each beta count and the separation of 210 Bi on the anion SPE disk at time t 9a . For a linear regression of the data: where A The 210 Bi activity (in dpm) per unit sample volume at time t 9a (A Bi t 9a ð Þ ) was calculated as where eff is the beta detector efficiency for 210 Bi expressed in units of cpm/dpm, yield is the fraction of bismuth recovered from the sample (as determined by the 207 Bi yield monitor), and vol is the initial sample volume. Between the time steps of collecting the 210 Pb,210 Bi, and 210 Po nuclides on the ferric hydroxide precipitate (t 8 ) and the separation of 210 Bi and 210 Po from 210 Pb on the anion SPE disk (t 9a ), an additional small correction can be applied for the decay of 210 Bi caused by any preferential scavenging of 210 Bi over 210 Pb by ferric hydroxide (where S Pb/Bi is the ratio of lead to bismuth scavenged). The corrected activity of 210 Bi at t 8 was calculated as where λ Pb is the decay constant for 210 Pb (8.51 × 10 −5 d −1 ), S Pb/Bi was taken as 1, and t is the time elapsed between time steps t 8 and t 9a . The S Pb/Bi value of 1 was based on analyses of duplicate lake water samples, where the ratio between the 210 Bi activity in secular equilibrium with 210 Pb in the water sample and the 210 Bi activity in secular equilibrium with 210 Pb in the saved eluate from SPE disk 3 was 95% AE 5% (n = 2). A Bi t 8 ð Þ represents the activity of 210 Bi in the S2 sample at the time of nuclide scavenging with ferric hydroxide. If the S2 sample was held for at least 30 d before processing, 210 Bi activities are assured to be at least 98.5% in equilibrium with their parent 210 Pb, assuming initial 210 Bi activities were zero. If initial 210 Bi activities in field samples were within 80% of secular equilibrium with 210 Pb at the time of sample collection (a likely scenario), then holding the S2 sample for 30 d results in final 210 Bi activities that are at least 99.7% in equilibrium with 210 Pb. This increases to 100.0% after 40 d.
A final small correction for the decay of total 210 Pb (A total Pb ) between time steps t 8 and sample collection at t 0 was calculated as where t is the time elapsed between time steps t 8 and t 0 . The propagated uncertainty of the estimate (σ A T

Pb
) was calculated as Uncertainties in the activity of total 210 Pb associated with the ratio of lead to bismuth scavenged by ferric hydroxide were negligible. 210 Pb particle-bound activity The activity of 210 Pb on particulate matter was calculated in a manner similar to the method described above for total over a significant fraction of the sample's 210 Bi lifetime, the 150-min measurements of gross beta activity (cpm) were plotted as a function of e −λBit , where t is the time elapsed between the start of each beta count and the separation of 210 Bi on the anion SPE disk at time t 9b . A linear regression of the data gave the initial activity of 210 Bi (A cpm Bi ) at time t 9b (Eq. 1). The 210 Bi activity (dpm) per unit sample volume at time t 9b (A Bi t 9a ð Þ ) was calculated using Eq. 2.
Because the loss of lead on the anion SPE disks was negligible (0.2% AE 2.1%; AE 1 SD, n = 4), and the sorption of bismuth on the disks was complete (99% AE 2%; AE 1 SD, n = 16) (as shown in the "Assessments: Materials and procedures" section below), the activity of particle-bound 210 Pb (A part Pb ) at the time of initial separation (t 2a ) on SPE disk 1 was calculated as where t is the time elapsed between the elution of 210 Pb on SPE disk 1 at t 2a and the separation of 210 Bi on SPE disk 4 at t 9b .
Because the time between t 2a and sample collection at t 0 was less than 1 d, A part Pb at t 2a was taken as A part Pb at t 0 . The propagated uncertainty of the estimate (σ A part Pb ) was calculated using Eq. 5. 210 Bi particle-bound fraction activity As with the lead fractions described above, repeated beta counts of the anion SPE disk 1 were plotted as a function of e −λBit , and the slope of the linear regression of the data gave the initial activity of 210 Bi (A cpm Bi ) at time t 2a (Eq. 1). The 210 Bi activity in dpm per unit sample volume at time t 2a (A Bi t 2a ð Þ ) was calculated using Eq. 2.
A small correction was applied for the decay of 210 Pb during the time elapsed between the separation of particles from the original sample matrix at time t 1a and the removal of 210 Pb at t 2a . The activity of 210 Bi in the particle-bound fraction (A part Bi ) of sample S1 at time t 1a was calculated as where t is the time elapsed between time steps t 1a and t 2a .
Because the time between t 1a and sample collection at t 0 was on the order of 1 h, A part Bi at t 1a was taken as A part Bi at t 0 . The propagated uncertainty of the estimate (σ A part Bi ) was calculated using Eq. 5. 210 Bi dissolved fraction activity Repeated beta counts of the anion SPE disk 2 were plotted as a function of e − λBit in the same manner as described above, and the slope of the linear regression of the data gave the initial activity of 210 Bi (A cpm Bi ) at time t 2b (Eq. 1). The 210 Bi activity (in dpm) per unit sample volume at time t 2b (A Bi t2a ð Þ ) was calculated using Eq. 2.
Two small corrections (< 1%) were applied for the decay of 210 Pb. Between the scavenging of the dissolved fractions of 210 Pb,210 Bi, and 210 Po on ferric hydroxide precipitate at t 1b and the removal of 210 Pb at t 2b ,~70% of the dissolved 210 Pb fraction that was scavenged by the precipitate was decaying to 210 Bi. The use of a 70% recovery value is based on three findings: (1) Rigaud et al. (2013) reported that scavenging of the dissolved lead fraction with Fe(OH) 3 in 80 seawater samples was consistently efficient at 70% AE 10%; (2) scavenging of 207 Bi with Fe(OH) 3 in this study averaged 60% AE 9% (n = 9), but included samples that were partially discarded after filtration slowed significantly (resulting in a lower yield); and (3) the Pb/Bi scavenging ratio in this study was~1 (see " 210 Pb total activity" section above). The corrected 210 Bi activity in the dissolved fraction (A diss Bi ) at t 1b was calculated as where the activity of 210 Pb in the dissolved fraction (A diss Pb ) was taken as A total Pb − A part Pb and t is the time elapsed between time steps t 1b and t 2b . The second correction for 210 Pb decay between the removal of particles at t 1a and t 1b accounted for the whole of the dissolved 210 Pb fraction contributing to 210 Bi activity. The corrected 210 Bi activity in the dissolved fraction (A diss Bi ) at t 1a was calculated using Eq. 8 and an A diss Pb multiplier of 1.0; t was the time elapsed between time steps t 1a and t 1b . Because the time between t 1a and sample collection at t 0 was on the order of 1 h, A diss Bi at t 1a was taken as A diss Bi at t 0 . The propagated uncertainty of the estimate (σ A diss Bi ) was calculated using Eq. 5. Uncertainties in the activity of dissolved 210 Bi associated with the ratio of lead to bismuth scavenged by ferric hydroxide were negligible. 210 Po activity The 210 Po activities of both particle-bound and dissolved fractions of sample S1 were determined by alpha counting the isotopes of 210 Po and the added yield monitor 209 Po. Both the yield of polonium recovered from the original sample and the alpha detector efficiency for 210 Po and 209 Po were calculated together as where A cpm 209 Po t7 ð Þ was the measured background-corrected activity of 209 Po (in cpm) at the start of the alpha count at time t 7 , and A209 Po t7 ð Þ was the activity of the added 209 Po standard (in dpm) at the start of the alpha count (t 7 ).
The activity of 210 Po (in cpm) at t 7 was corrected for background and decay during the count as where count210 Po was the gross alpha count, bg 210 was the measured background in the 5.31 MeV region, λ Po is the decay constant for 210 Po (5.7975 × 10 −8 s −1 ), and t was the length of the alpha count (s). The 210 Po activity (in dpm) per unit sample volume at time t 7 was calculated as where vol is the initial sample volume. Because bismuth was scavenged along with polonium on the anion SPE disks, and 210 Bi decayed to 210 Po before polonium separation, a final correction for both 210 Bi and 210 Po decay to the time of the initial separation on the SPE disks was calculated as where 210 Po particle-bound fraction activities at t 2a (A part Po t 2a ð Þ ) and dissolved fraction activities at t 2b (A diss Po t 2b ð Þ ) used corresponding particle-bound and dissolved 210 Bi activities, and t was the time elapsed between time steps t 7 and t 2 . Because the time between t 2a,b and sample collection at t 0 was less than 1 d, A Po at t 2a,b was taken as A Po at t 0 .
The propagated uncertainty of the estimate (σ APo ) was calculated as where σ A cpm

Assessment: Materials and procedures
Anion SPE disk sorption efficiencies

Bismuth
The efficiency of bismuth retention on the anion SPE disks was determined using 207 Bi (Fig. 3). In rain, mussel tissue, and particle-bound water fraction samples, where the transfer of the 207 Bi spike to the SPE disk was complete, the first elution for the measurement of 210 Bi (Fig. 3, filled circles) showed 207 Bi recoveries of 100% AE 2% (AE 1 SD, n = 9). The eluate of these samples was saved for 210 Pb analysis (via the ingrowth of 210 Bi) and spiked once more with 207 Bi. The second elution (Fig. 3, open circles) again showed 207 Bi recoveries of 99% AE 2% (AE 1 SD, n = 7). From these results, I conclude that the anion SPE disks are essentially 100% efficient at scavenging bismuth.

Lead
Four digested sediment samples (with 210 Bi in equilibrium with 210 Pb) were run through SPE disks and repeatedly beta counted. The beta counts were plotted against the decay time (e − λBit ) so that the slope of the linear regression gave the 210 Bi activity (cpm) at the time of elution (Fig. 4, nablas). After 57 d (i.e.,~11 half-lives of 210 Bi), the sample eluates (containing any 210 Pb that passed through the first set of SPE disks) were run through a second set of SPE disks and the disks were repeatedly beta counted to determine the 210 Bi activity in secular equilibrium with 210 Pb (Fig. 4, circles). Differences in the activities (slopes) of 210 Bi in the original samples and the 210 Bi (in equilibrium with 210 Pb) in the sample eluates averaged −0.01 AE 0.07 cpm (AE 1 SD, n = 4). If I also consider the decay of 210 Pb over the 57-d ingrowth period, relative differences between the original and eluate activities shrank to 0.2% AE 2.1% (AE 1 SD, n = 4). Had any significant amount of 210 Pb Fig. 3. Recovery of the 207 Bi yield monitor on anion SPE disks. Line shows 100% recovery. Filled circles show the recovery of the first 207 Bi spike for 210 Bi. Open circles show the recovery of the second 207 Bi spike in sample eluate aged for 210 Pb analysis. R, rain samples; LS, suspended particulate matter samples; M, mussel tissue samples.
sorbed to the SPE disks during the first elution, the activities of 210 Bi in the second elution disks should have been lower than the first. From these results, I conclude that the sorption of lead to the anion SPE disks is negligible.

207
Bi gamma efficiency Plates with the NIST-calibrated 207 Bi standard were prepared according to the method described in "Materials and procedures" section. The two detector efficiencies for the 569 keV peak were 0.0272 AE 0.0010 and 0.0346 AE 0.0012 cpm dpm −1 , respectively. The relative uncertainty in efficiency for both detectors averaged AE 3.5%.

207
Bi beta efficiency Because gamma counting efficiencies are, in general, low, it is tempting to speed up bismuth yield analysis and sample throughput by increasing the 207 Bi activity of the yield monitor. However, internal conversion processes associated with 207 Bi decay release high-energy electrons that register as beta counts in the proportional counter.
To examine the effect of 207 Bi activity on gross beta activity, four samples containing 4.79 AE 0.02 dpm of 210 Bi were spiked with 0, 17.6, 35.5, and 71.0 dpm of 207 Bi. The samples were run through anion SPE disks and the disks were repeatedly beta counted over a period of several weeks (Fig. 5). The mean slope of all four counts (indicating initial 210 Bi activities at time of separation on the SPE disks) was 2.195 AE 0.026 cpm (AE 1 SD, n = 4), with a standard deviation of the mean (AE 0.026 cpm) smaller than the individual standard errors of each slope (Fig. 5A). This demonstrated that the activity of the 207 Bi yield monitor does not interfere with the calculated activity of 210 Bi. However, the uncertainty of each 210 Bi estimate (AE 1 SD) is taken as the standard error of the slope, and this did increase with increasing 207 Bi activity (Fig. 5B). The increase in the standard error of the slope amounted to 0.0004 AE 0.00004 cpm per dpm of 207 Bi. In practical terms, for a sample with a total 210 Bi activity of~5 dpm, a 207 Bi spike of 35.5 dpm (0.6 Bq) added approximately~1% to the total relative error of the sample activity estimate when compared to a sample with no 207 Bi spike. e -λt Fig. 4. Sorption of 210 Pb on the anion SPE disk. Four samples containing 210 Bi in secular equilibrium with 210 Pb were passed through separate SPE disks twice. Blue nablas show initial 210 Bi activity (slope m). Red circles show 210 Bi activity (slope m) in equilibrium with 210 Pb in aged eluate from first filtration.  Bi beta efficiency Calibration curves for 210 Bi beta efficiencies in three of the four detectors used to measure 210 Pb and 210 Bi activities in environmental samples are shown in Fig. 6. Each curve was composed of eight calibrated samples, and the same eight samples were counted in each detector. Four of the eight standard samples were derived from a solution of digested lake sediment that was calibrated using the NIST-calibrated 210 Po standard (Fig. 6, filled circles). The other four standard samples were made using the NIST-calibrated 210 Pb standard (Fig. 6, open circles). 210 Po and 210 Bi were in secular equilibrium with 210 Pb in both the sediment-derived and 210 Pb standards. 207 Bi recovery in the sediment-derived standard samples averaged 99.5% AE 1.7% (AE 1 SD, n = 4). A uniform recovery of bismuth was also indicated by the low standard error of each slope estimate in Fig. 6 (< 3% relative error). 210 Bi beta efficiencies (eff) were taken as the slope of each calibration curve and averaged 0.504 AE 0.004 cpm dpm −1 (AE 1 SD, n = 3) for Detectors 1b, 1c, and 1d. The fourth detector used for environmental sample analysis (i.e., Detector 2a, not shown) had a 210 Bi beta efficiency of 0.506 AE 0.017 cpm dpm −1 .
The y-intercept of each calibration curve for all four detectors used for environmental sample analysis (i.e., those shown in Fig. 6 and Detector 2a) averaged 0.019 AE 0.108 cpm and did not differ significantly from zero. This indicated that blank background activities of 210 Pb,210 Bi,and 210 Po in, for example, anion SPE disks, nitrocellulose filters, and reagents were negligible at least as far back as procedural time step t 1b .
The concordance between slopes of both sediment-derived and 210 Pb standards gave credence to both the accuracy of the NIST-calibrated standards and that my α-, β-, and γ-counting procedures were synchronized (in the sense that the activity of 210 Bi as determined by α-counting 210 Po in equilibrium with 210 Bi was equal to the activity of 210 Bi as determined by βand γ-counting).  210 Pb standard. 210 Pb,210 Bi,and 210 Po in secular equilibrium in both standards. Slope (m) indicates detector efficiency. Slope intercept (y 0 ) indicator of procedural background.

Field sample collection
Environmental samples of rain, lake water, and dreissenid (quagga) mussels were collected from the University of Wisconsin-Milwaukee School of Freshwater Sciences campus and its adjacent slip in the Milwaukee Inner Harbor (Fig. 7). The slip measures 365 m long and 29 m wide, with an average water column depth of 4 m.
Rainwater was collected at ground level (43.017719 N, 87.903000 W) in a large plastic barrel fitted with a funnel (0.216 m 2 collection area) over a 40-h period during an extended rain event beginning at 17 : 20 on 03 November 2018. The funnel and barrel were rinsed before and after the collection event with a total of 0.4 L of 1 M HCl.
Duplicate lake water samples (~50 L) for radionuclide analyses were collected from the slip (43.017835 N, 87.903521 W) with a submersible pump from a depth of 2 m on 15 November 2018 and 20 November 2018.
Quagga mussels were collected from the slip wall (43.017829 N, 87.904407 W) on 29 November 2018. Each mussel was measured for shell length and sorted into two groups of large (range: 18-22 mm; geometric mean: 19 mm; n = 10) and small (10-16 mm; geometric mean: 13 mm; n = 20) mussels. Mussel tissue was separated from the shell, pooled by group into two glass beakers, and digested in concentrated HNO 3 . Shell-free biomass was estimated using the allometric equation m = 0.0018 × L 3.11 , where m is the tissue dry weight in mg (DW mg) and L is the mussel shell length in mm .

Field sample activities
Rainwater A total of 5.39 L of rainwater was collected and split into two samples for replicate analyses. Mean total activities (AE mean absolute deviation [MAD]) of 210 Pb,210 Bi,and 210 Po were 16,984 AE 357, 10,000 AE 40, and 873 AE 20 dpm m −3 , respectively (Rain A and Rain B; Table 1). Relative errors between replicate analyses were 2.1%, 0.4%, and 2.3%, respectively. Mean 210 Pb : 210 Bi : 210 Po activity ratios in rainwater were 1 : 0.59 : 0.05. Similar activities and activity ratios of 210 Pb,210 Bi,and 210 Po have been reported in rain over Japan (Tokieda et al. 1996).

Lake water
Particle-bound, dissolved (< 0.45 μm), and total activities of 210 Pb,210 Bi,and 210 Po in lake water on 15 November and 20 November are shown in Table 1. Relative MADs of duplicate sample analyses of lake water were 2.4% AE 1.9% for 210 Pb (geometric mean of total sample activity: 3.0 dpm, n = 6), 7.7% AE 5.8% for 210 Bi (geometric mean of total sample activity: 2.6 dpm, n = 8), and 2.7% AE 1.7% for 210 Po (geometric mean of total sample activity: 1.4 dpm, n = 8), and compared favorably to the precision of other methods employing α-spectroscopy for the analysis of 210 Po and the determination Table 1. Activities of 210 Pb,210 Bi,and 210 Po in rain and lake water.

Sample
Type a Collected date (2018) 210  of 210 Pb via the ingrowth of 210 Po (e.g., Church et al. 2012;Baskaran et al. 2013;Rigaud et al. 2013). The relative propagated counting errors for all three nuclides averaged 7% AE 3% (n = 22). Importantly, the relative MADs for all 11 pairs of duplicate samples averaged 4% AE 4% (n = 11), which gave some indication that all significant counting errors were being considered.
The total 210 Pb activity of 105 dpm m −3 on 20 November and the range of total (dissolved + particle-bound) 210 Po activities from 56 to 58 dpm m −3 on 15 November and 20 November were in general agreement with other reported activities of total 210 Pb and 210 Po in Lake Superior (48-131 and 16-54 dpm m −3 , respectively; Chai and Urban 2004), the Clinton River in Michigan (90-684 and 78-438 dpm m −3 , respectively; Mudbidre et al. 2014), and Crystal Lake in Wisconsin (113 AE 40 and 95 AE 47 dpm m −3 , respectively; Talbot and Andren 1984).
The total (dissolved + particle-bound) 210 Bi activity of 88 dpm m −3 and total 210 Bi/ 210 Pb activity ratio of 0.84 on 20 November is significant because it shows, for the first time, a substantial disequilibrium between the daughter and parent in the water column (see Tokieda et al. 1994;Biggin et al. 2002).

Mussel tissue
Activities of 210 Pb,210 Bi,and 210 Po in quagga mussel tissue are shown in Table 2. Mean activities (AE MAD) of 210 Pb,210 Bi,and 210 Po in both small and large mussel samples were 2.8 AE 0.4, 0.7 AE 0.3, and 43 AE 3 dpm DW g −1 , respectively, with nuclide activity ratios of 1 : 0.3 : 15.4. The 210 Po activity in mussel tissue was roughly 1.7 times higher than what was found on suspended particulate material on 20 November (i.e., 26 AE 1 dpm g −1 ; J. T. Waples unpubl.). The enhanced bioconcentration of 210 Po is commonly observed in marine organisms (e.g., Stewart and Fisher 2003).
By comparison, mean 210 Pb and 210 Po activities in (Mytilus) mussels from the Atlantic coast of Portugal were remarkably similar at 3 AE 1 and 46 AE 17 dpm g −1 , respectively, with a 210 Po/ 210 Pb activity ratio of 16.9 (Carvalho et al. 2011). Similar 210 Po/ 210 Pb activity ratios have been found in bivalves from, for example, the Aegean coast of Turkey (U gur et al. 2002) to the western English Channel (Connan et al. 2007).
The low activities of 210 Bi in quagga mussel tissue ( 210 Bi/ 210 Pb:~0.3) are consistent with the study by Fowler et al. (2010), which found a bismuth assimilation efficiency of only~4% in copepods fed with 207 Bi-labeled phytoplankton, and another study by Noshkin et al. (1984), which found whole fish 210 Bi/ 210 Pb activity ratios of~0.4 in composite samples made up of bone, mussel, and liver tissue from the Bikini and Rongelap Atolls.

Discussion
The method described here (as modified from Marley et al. 1999) allows for quick measurement of 210 Pb,210 Bi,and 210 Po in aquatic samples and should enable the radiotracer community to determine: (1) if the 210 Bi/ 210 Pb nuclide pair can serve as a useful tracer for short-term scavenging processes in the upper water column (Fowler et al. 2010) and (2) whether or not the scavenging of 210 Bi can significantly alter particle flux estimates derived from 210 Po/ 210 Pb disequilibrium (Kim and Hong 2019).
This method fundamentally differs from current methods to measure 210 Po and 210 Pb in that instead of measuring 210 Pb via the ingrowth of 210 Po (e.g., Church et al. 2012, references therein), 210 Pb is measured via the decay of isolated 210 Bi that was in secular equilibrium with 210 Pb. An immediate benefit of this approach is that 210 Pb can be determined after 1 month instead of > 6 months. The method described here also eliminates the need for a lead yield monitor, which can be a significant source of background 210 Po and 210 Pb (Rigaud et al. 2013).
Early studies of 210 Pb in the environment included methodologies where 210 Pb was determined by the ingrowth of 210 Po (e.g., Burton and Stewart 1960;Hill 1960;Holtzman 1966;Shannon et al. 1970) as well as 210 Bi (e.g., Blifford et al. 1952;Burton and Stewart 1960;Rama and Goldberg 1961;Fry and Menon 1962;Craig et al. 1973). Comparisons of the two approaches showed similar levels of precision. Burton and Stewart (1960) estimated the precision of their 210 Bi technique at approximately AE 10% and their 210 Po technique at < AE 15%, although it is not immediately clear if total sample activities in both sample sets were similar. An intercomparison of 210 Pb measurements at GEOSECS station 500 showed that the 210 Bi technique for measuring 210 Pb had a precision of 5% for total sample activities of~4 dpm 210 Pb (Chung et al. 1983). A follow-up study showed the precision of the 210 Po technique for measuring 210 Pb ranged from~2% to 15% for total sample activities of~1-3 dpm 210 Pb, (Fleer and Bacon 1984).
A significant constraint of this method (and the measurement of all short-lived nuclides, including 210 Po) is the necessity to rapidly separate and count the nuclides. In this study, the shore-based processing of a~50 L water sample took an Table 2. Activities (AE 1 SD) of 210 Pb,210 Bi,and 210 Po in dreissenid (quagga) mussels.

Sample
Collected date (2018) 210 Pb dpm g −1 210 Bi dpm g −1 210 Po dpm g −1 Small mussel tissue 11/29 3 AE 2 0 AE 1 4 6 AE 1 Large mussel tissue 11/29 2 AE 1 1 AE 1 3 9 AE 1 average of 8 h-from sample collection to starting the 210 Bi β-count. This included filtration of both particulate and dissolved sample fractions, acid digestion of both fractions, and nuclide separations on an anion SPE disk, with acid digestion taking the longest amount of time. Offshore applications of this method will require shipboard processing of samples; and the use of strong acids for sample digestion will necessitate the availability of a chemical fume hood (Rigaud et al. 2013).
Microwave digestion of samples could reduce both the volume of acid used and time of digestion considerably (e.g., Michel et al. 2008;Szarlowicz 2019) and should be considered in our evolving approach to measuring 210 Pb,210 Bi, and 210 Po in aquatic systems.

Comments and recommendations
This method is amenable to any modification in sample pre-treatment or polonium analysis (see http://www.geotraces. org/sic/intercalibrate-data/cookbook; last accessed on 23 August 2019). It may be preferable, for instance, to use ferric chloride instead of ferrous sulfate to create a ferric hydroxide precipitate so as to prevent the precipitation of calcium sulfate in a seawater sample.
If sample volume or storage space is limited, and the collection of a separate (S2) sample for total 210 Pb is impractical, then a stable Pb yield monitor (Rigaud et al. 2013) should be added to the S1 sample so that the in situ dissolved 210 Pb fraction can be quantified using the eluate from SPE disk 2 (time step t 2b ).
Because anion exchange is selective (e.g., Saito 1984), other beta emitting radionuclides that might also sorb to the anion SPE disk and interfere with the determination of 210 Bi activity are not likely to be encountered in offshore waters. When sampling in coastal waters near large urban centers, however, several short-lived radiopharmaceuticals in treated sewage effluent could sorb to the SPE disk and spuriously increase beta counts attributable to 210 Bi activity. Of special concern is the beta emitter, iodine-131 ( 131 I t 1/2 : 8.01 d) (e.g., Montenero et al. 2017). For this reason, it is good practice to confirm that beta activity is decaying at a rate that is consistent with 210 Bi by fitting beta decay as a function of time with a threeparameter exponential decay curve, where the fitted decay constant (λ) should equal the expected 210 Bi decay constant of 0.13835 d −1 .