Initial Testing to Establish Experimental Conditions

Several approaches were considered to establish the most appropriate conditions for testing turbidity corrections for fDOM measurements by maximizing the turbidity range while minimizing inner-filtering effects. Fluorescence properties are known to change in environmental conditions and water samples over time. Previous testing of fDOM corrections used a prepared organic matter standard, with materials obtained from the International Humic Substances Society (IHSS; St. Paul, Minnesota; http://www.humicsubstances.org). The previous work used Suwanee River natural organic matter (SRNOM; IHSS reference standard 2R101N) for inner-filtering effect corrections and a sediment standard, Elliot Silt Loam (ESL; IHSS reference standard 1BS102M), for the turbidity correction. SRNOM provides a stable DOM solution, particularly in the fluorescence region measured by the fDOM EXO sensor but has a lower than ideal pH (less than 4) for fluorescence measurements (Groeneveld and others, 2022). In the test, the solution was stable and prepared from mixing the highly organic ESL standard with organic free water (OFW), which has a pH of 6.5 to 7 that is ideal for fluorescence measurements.

To test for turbidity interferences, manufacturers typically use turbidity standards as the light scattering matrix. Although these standards scatter light and provide a good calibration for the scattering-based turbidity measurement, they do not represent the full effects of natural, suspended particles that interfere with the fDOM measurement because natural particles scatter light differently and can also absorb significant amounts of light. Therefore, it is likely that the use of these artificial (plastic beads, formazin) turbidity standard matrices for testing fDOM interference results in an underestimate of the effects of turbidity on the fluorescence measurement and leads to erroneous conclusions about turbidity effects on the sensor measurement.

Another approach used in turbidity interference testing is to add particles (for example, diatomaceous earth, purified silt, or sand) to a natural water sample and measure the extinction of the fDOM response. The concern with this approach is that the added particles can interact with DOM from the solution, which may result in the alteration of the DOM in the solution via selective absorption to the particle surfaces. Once sorbed, the fluorescent properties may differ in solution as may the absorption properties of the particles, resulting in a poor correction for natural particles. Although no approach is ideal, the experiment completed here sought to minimize the effects of mixing solutions and particles that could interact physically or chemically with each other. For these experiments, the starting suspension was prepared using the ESL standard in OFW. Different concentrations of ESL were tested to achieve a high-turbidity solution while minimizing inner-filtering effects.

Initial testing was performed in black 5-gallon buckets to obtain the ideal concentration for the experiments. The experiment started with 16,000 milligrams (mg) of ESL into 8 liters (L) of OFW for a concentration of 2,000 mg/L. The concentration was then increased by an additional 2,000 mg/L stepwise to a maximum of 10,000 mg/L ESL seeking the balance of high turbidity with relatively low inner filtering. Once the concentration was identified, the sondes were suspended in the solution with various clamps, stands, and zip ties to determine the best method of suspension and sensor layout in the larger mixing tank (fig. 1). Data was logged from these sensors over the duration of each test to determine:

Filtration Tests

The full experiment was completed during 3 separate days using a different group of sensors in each experimental run (fig. 2). Sensors and equipment were set up and calibrated in accordance with the manufacturer’s guidance (https://www.ysi.com/exo-university/category/exo-sensor-calibration). Each sensor passed the calibration quality check reported by the KOR software SmartQC Score before use in all laboratory experiments. Measurements from the full filtration experiments are available in Baxter and others (2023). Full filtration experiments were done on August 8, 2022; August 11, 2022; and January 12, 2023.

Solutions were prepared on a Monday or Thursday to allow the ESL solution to reach equilibrium over a 3-day period of mixing. An EXO was placed in the 100-L tank with two submersible pumps to circulate the solution throughout the equilibration period to confirm turbidity levels were maintained and fDOM equilibration was achieved during the pre-measurement period. On the fourth day, the remaining sensors were deployed in the tank to begin logging measurements each minute throughout the filtration experiment.

Two capsule filters (0.45 micrometer; Pall-12179; Pall Corporation, Port Washington, New York) were attached to peristaltic tubing and flushed with 2 L of OFW and drained before use (process hereafter referred to as “conditioning”). After conditioning, the filters recirculated water from the resuspension tank directly back into the bin to remove turbidity slowly and continuously from the solution until the turbidity was lowered to less than 5 FNU. When the filtration lines’ flow slowed from a steady stream to dripping, a new capsule filter was conditioned and replaced on the clogged filter line. Each line required at least two filter changes over the course of each experiment, which lasted for several hours. Filtered water samples were collected from the recirculation line at three time points throughout each experiment day to collect independent measurements on the benchtop fluorometer to ensure minimal changes in fluorescence occurred in the filtrate throughout the filtration experiment. Data from the 3 experiment days can be found in Baxter and others (2023).

Exponential Approaches to Fluorescent Dissolved Organic Matter Corrections

To investigate the possibility that the change in fDOM sensor manufacturing affected corrections, the correction approach used by Downing and others (2012) was followed initially, in which the fraction of fDOM measurements relative to the fully filtered fDOM measurement (fDOMfilt) was plotted against the turbidity across the filtration experiments (fig. 5). A two-parameter (2P) exponential fit was applied in Excel software (Microsoft, Redmond, Washington) using the standard exponential fit:

USGS staff generate the turbidity corrections in the form of a one-parameter (1P) exponential fit of the equation, as presented in Downing and others (2012), which sets b=1 when calculating the exponential fit. In previous guidance (Booth and others, 2023), the calculation uses the variable name ρ instead of c; this report uses c for consistency among the different fitting equations presented here. When replicating this approach, the exponential coefficient, c, varied from −0.0043 to −0.0061 among the serial numbers tested with no systematic trend over time (table 6), suggesting that manufacturing changes did not affect the corrections. Because Downing and others (2012) did not explicitly report exponential coefficient (c or ρ) values, it is difficult to report whether the coefficients for these sensors differ markedly from those of the prior generation of fDOM and turbidity sensors. However, the exponential term c has typically been reported between −0.003 and −0.006 (Booth and others, 2023), and the value reported here for the regression using all pooled data (−0.0049) compares well with this range of previously reported values.

Although there was no evidence that fDOM sensor corrections differed by manufacture date (as indicated by the serial numbers), the results raised some larger questions about the current method for applying turbidity corrections to fDOM measurements. The correction guidance in Booth and others (2023) often leads to a poor exponential fit at high turbidity because the 1P exponential approximation does not effectively capture the shape of the fDOM extinction curve (fig. 6). This issue is minor for low turbidities (less than 100 to 200 FNU) where the approximation provides a reasonable fit; however, the issue becomes significant in systems with higher turbidities. This finding also highlights the need for a correction covering the full range of the turbidities encountered at a site because the coefficient is strongly affected by the highest turbidity value.

To address the poor fit to the measured data curvature, other studies have tried to split data into bins (Regier and others, 2020). This approach may generate better corrections over a wider turbidity range but often causes large discontinuities at the binned turbidity break points (fig. 6), resulting in stepwise offsets at the arbitrarily assigned turbidity thresholds that can lead to noisy time series records. Fitting multiple, smaller intervals of turbidity (for example, 100 FNU bins) would likely minimize discontinuities and provide a better correction across a wider range of turbidities but complicates the corrections process and presents a challenge to quality assurance. A better approach is needed to effectively correct fDOM in higher turbidity systems.

To find a better correction approach, a wide range of empirical fits to the filtration experiment data were evaluated, including the two aforementioned exponential fits (1PXL and 2PXL) and four exponential fits (2PJ, three parameter [3PJ], four parameter [4PJ], and five parameter [5PJ]) generated using a statistical software package (version 13.0, JMP Statistical Discovery LLC, Cary, North Carolina). Previous corrections for field-based data reported using a 3P exponential fit (Lee and others, 2015; Saraceno and others, 2017; Regier and others, 2020) in the form:

The various exponential fits performed in the statistical software all appeared to fit the pooled data for the 11 sensor combinations well based solely on R ² values (fig. 7); however, the 2PJ exponential fit did not match the curvature well and yielded a scale factor equal to around 50 times at a turbidity of 650 FNU. The 3PJ exponential fit better fit the curvature and yielded a scale factor of only around 7 times at 650 FNU, nearly an order of magnitude scale factor less than the 2PJ correction. The 4PJ and 5PJ biexponential models appeared to fit the data best across the full turbidity range and yielded similar scale factors of 10 to 12 times at 650 FNU, but the 5PJ had the lowest root mean square error (RMSE), suggesting it was the best fit (fig. 7). The sensor-specific fits for individual sensor combinations were generally consistent, but there were variations among sensor combinations with respect to the model terms (a, b, c, d, e) for the correction equations that warranted further evaluation (table 7).

The approach used to evaluate the fDOM corrections among sensor combinations was to apply the corrections across the measurements in the filtration tests. Many of the corrected fDOM records showed minimal variability and appeared stable with slopes near zero across the turbidity range for both the pooled correction and the sensor-specific correction (table 8). The 2PJ exponential fit showed visual differences from the 2PXL exponential fit (fig. 8). Of all the fDOM-turbidity sensor combinations, four corrected records did not differ between the pooled correction and the sensor-specific correction (fig. 8), whereas three combinations had minor differences between the pooled corrections and the sensor-specific corrections (fig. 9). Of those that had minor differences, fDOM sensor 15A100346 had negative values at high turbidities, indicating a poor calibration. Although the slope across the corrected fDOM values was near zero, there was greater variability than desired in the pooled equation corrected values (fig. 9A), likely attributable to a poor calibration or possibly sensor drift. Sensor combinations 17K104814-17G102898 and 19M101717-22E100475 from the August 8, 2022, test had higher than desired slopes (figs. 9C, 9E). In all three cases where the slope was higher than desired, the sensor-specific corrections performed well (figs. 9B, 9D, 9F), likely reflecting sensor drift or possibly a poor calibration.

The remaining four sensor combinations were evaluated more closely because of the age of two of the turbidity sensors (greater than 8 years) contributing to three sensor combinations, and one turbidity sensor (20K103202) being manufactured within the range of sensors that had been flagged for possible drift regardless of age (Xylem, Inc., 2022). Turbidity sensors manufactured within this range may experience a high level of drift while deployed. To evaluate the potential effect of these three turbidity sensors on the fDOM corrections, the turbidity measurements were replaced with a different turbidity record from the same filtration test but on a different sonde.

The corrected fDOM measurements from the first sensor combination in this group (20H103551; 14G102122) were highly variable across the full turbidity range for both the pooled and the sensor-specific corrections (figs. 10A, 10B). When the fDOM measurements for sensor 20H103551 were corrected using measurements from another turbidity sensor (18E105140) from the same test run, the pooled correction yielded stable corrected fDOM measurements across the full turbidity range (fig. 10C; table 9).

The corrected fDOM measurements from the second sensor combination in this group (22D101246, 20K103202) included a turbidity sensor within the manufacturing range when drift was a concern among new sensors (March 2019 through July 2021; serial numbers 19C104566 through 21H100299) but had not been identified previously during calibration. The corrected fDOM measurements using the pooled correction showed evidence of drift with a slope of −0.02 across the turbidity range of the filtration test (fig. 10D). The corrected fDOM measurements from the sensor-specific correction were stable with a zero slope (fig. 10E). When the 20K103202 turbidity record was replaced with the record from turbidity sensor 18E105140, as above, the corrected fDOM measurements using the pooled correction improved such that the slope was less than the 0.02 threshold applied (fig. 10F)—although the corrected fDOM measurements had greater variability than the sensor-specific correction, as would be expected for a separate instrument, even in a well-homogenized tank.

The other two combinations in this group included the turbidity sensor 13L102366, the oldest sensor used in the study. The fDOM sensor 19D104178 paired with 13L102366 turbidity sensor had a slope of nearly 0.05 across the turbidity range in the August 8, 2022, filtration test (fig. 10G). The corrected fDOM measurements using the sensor-specific correction showed less variability and a lower slope (fig. 10H). When the 13L102366 turbidity measurements were replaced with those from turbidity sensor 22E100475, there was improvement in the slope across the turbidity range (from nearly 0.05 to 0.03) but did not meet the criteria (slope less than 0.02) for a good correction (fig. 10I).The fDOM sensor 19D104178 was recalibrated and used in another filtration test (January 12, 2023) with a different turbidity sensor resulting in a good fDOM correction using the pooled correction equation (fig. 8C). The poor fDOM correction for the 19D104178-13L102366 sensor combination in the August 8, 2022, filtration test (fig. 10G, 10H) appeared to be caused by both the drift in the old turbidity sensor and a poor fDOM calibration.

The effect of potential drift in turbidity sensor 13L102366 on the correction to fDOM sensor 16G102723 measurements was not quantifiable. This fDOM sensor had negative values at high turbidities and required a baseline offset to process the data, similar to fDOM sensor 15A100346; however, the effect of the fDOM calibration differed. Whereas the calibration correction for sensor 15A100346 appeared to follow a step adjustment across the range of fDOM measurements, the calibration for 16G102723 appeared to be a scale adjustment across the fDOM range, leading to a slope of −0.06 across part of the turbidity range of the test with a steep upward curve at higher turbidities using the pooled correction (fig. 10J). The fDOM correction using the sensor-specific correction generated a stable record, but the effect of the offset was observable at the higher turbidities (fig. 10K). When the turbidity measurements from sensor 13L102366 were replaced with another turbidity record (22E100476), the fDOM correction did not improve but worsened because the turbidity drift compounded the deviation caused by the fDOM calibration issue (fig. 10L). Despite the age of the 13L102366 sensor and some evidence of drift, it appeared to have minimal effect on the fDOM corrections relative to the issues imparted by the apparent errors in fDOM sensor calibrations.

Two other fDOM sensors were used in two different filtration tests, 19M101717 and 22E100475, in the August 8, 2022 (figs. 9E, 9F), and August 11, 2022 (fig. 8D), tests, for which the same fDOM calibration was used, and 17K104814 and 17G102898 in the August 8, 2022 (figs. 9C, 9D), and January 12, 2023 (fig. 8A), tests, for which the fDOM sensor was recalibrated between the tests. In both cases, the fDOM corrections were stable with low slopes (less than 0.02) across the range of turbidities in the August 11, 2022, and January 12, 2023, tests, but the pooled corrections had elevated slopes (0.02–0.03) across the turbidities in the August 8, 2022, test (figs. 8, 9). These differences were relatively minor compared to the scale of the fDOM corrections across the turbidities tested. The only factor that changed among the tests was the 2,500-mg ESL in the August 8, 2022, test versus the 2,000-mg ESL in the August 11, 2022, and January 12, 2023, tests. Further testing should attempt to quantify the effect of concentration on the corrections.

Non-Exponential Approach to Fluorescent Dissolved Organic Matter Corrections

The alternate approach to fitting the fDOM-turbidity curves without exponential fits performed well (table 10; fig. 11). The inverse polynomial fit (IPF) was best fit with a quadratic equation of the form:

The resulting fDOM corrections were comparable to the biexponential 5P fit (table 8). One benefit of this approach over the exponential approach is that the sensor combinations with poor fDOM corrections were immediately identified by simply plotting the data and thus were easily flagged for review (fig. 11). This finding is likely because the fDOMfilt/fDOMwt metric more effectively exposes the calibration deviations at the low end of the measured fDOM, where the fit to the data carries more weight compared to the fDOMwt/fDOMfilt metric. Because this approach identified data of poor quality earlier in the process, it may serve as a tool to screen sensor performance. Further evaluations are warranted to determine the robust/stable nature of the quadratic fit and its potential utility as a sensor quality assurance screening tool.