Performance assessment of serial dilutions for the determination of backscattering properties in highly turbid waters

The ECO BB9, an instrument designed for characterizing the particulate backscattering coefficient (bbp) of waters in situ, saturates frequently in water with high concentrations of particles. These water types are of increasing interest in water optics research due to the complexity of their contents and gaps in the knowledge of their interactions with the light field. Through serial dilutions, the concentrations of particles can be brought into the instrument range and linear extrapolation can be used to yield a prediction of bbp for the original undiluted solution. The efficacy of this simple approach is explored here using natural and synthetic waters in a controlled laboratory setting. bbp is a key inherent optical property used in validating and calibrating water quality parameters commonly estimated by remote sensing inversion algorithms. For this reason, the synthetic waters were constructed to test the method across water types characteristic of colored dissolved organic matter, non‐algal particulates, and phytoplankton. The dilution method was evaluated by assessment of dilution series accuracy, precision, and constancy of the backscattering spectral slope. It was found to be effective with all water types in this paper.

The particulate backscattering coefficient (b bp ) is an inherent optical property (IOP) that describes how light is scattered at angles greater than 90 by the particulate constituents in water (Sullivan et al. 2013). b bp is influenced by the morphology, refractive index, and concentration of particles (Mobley 1994;Morel 1974;Bohren and Huffman 2008). Accurate characterization of b bp with known particulate assemblages has applications in many areas of oceanography including the capability for space borne sensors to infer types and quantities of particles in water (Neukermans et al. 2012). In situ IOP measurements are used in the calibration and validation of remote sensing data and the optical models designed for retrieval of particle concentrations in water (IOCCG 2000).
Development and implementation of relationships between b bp , measured with in situ sensors, and particulate assemblages in natural waterbodies is widely used in ocean color research. The WetLabs ECO BB9 measures the volume scattering coefficients (β [θ,λ]), in m À1 sr À1 , at the angle 124 at nine wavelengths from which b b and b bp can be derived (Buiteveld et al. 1994;WETLabs 2007;Doxaran et al. 2016). The ECO BB9 is extensively used in optical oceanography and designed with a dynamic range suited for clear oceans, limiting the measurable range of naturally occurring scattering properties (Doxaran et al. 2016). Recently, these instruments are also being used in complex freshwater and estuarine environments, characterized by higher concentrations of colored dissolved organic matter (CDOM), and scattering particles including phytoplankton (Stephanie et al. 2015). Consequently, ECO BB9 saturation has been noted in numerous studies of scattering in particle-rich natural waters (McKee et al. 2009;O'Donnell et al. 2010;Slade and Boss 2015;Doxaran et al. 2016), resulting in incomplete IOP observations for some turbid natural waters. Given the importance of accurate IOP characterization in resolving bio-optical models and in the calibration and validation of remote sensing data, effective methods to measure b bp in such extreme waters will improve remote sensing applications and their larger scale *Correspondence: gemma.kerrisk@csiro.au Author Contribution Statement: G.K., N.D., P.F., H.B., and J.A. have played crucial roles in the conception and design of the project or output. They have all been responsible for the acquisition of research data, where their expertise and intellectual judgment were necessary for planning and design. In addition, they have contributed valuable knowledge, including Indigenous knowledge, where it was deemed relevant. Furthermore, all authors have been instrumental in the analysis and interpretation of research data. They have either drafted significant portions of publications or have provided critical revisions to contribute to their interpretation. The contributions of these individuals have been invaluable in the successful execution of this output.
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.
It is possible to change the ECO BB9 range with a fixed gain modification or use alternate sensors such as the Hobi labs HydroScat-6P and Sequoia Scientific's Hyper-bb as they are better suited to handle the increased particle concentrations. However, altering the gain of the ECO BB9 sensor can be expensive and is not always feasible. For example, when conducting a transect from freshwater to seawater, where the freshwater sites are beyond the measurable range, a modification to accommodate these conditions is likely to restrict the functionality of the sensor in clear seawater conditions. The HydroScat-6P is no longer available for purchase and the Hyper-bb, while promising, is relatively new and dynamic ranges were not available (Sequoia Scientific 2023). In addition, the HydroScat-6P relies more on assumptive corrections than the ECO BB9, due to its longer pathlength (Doxaran et al. 2016). Doxaran et al. (2016) demonstrated the HydroScat-6P pathlength to be a key issue in highly scattering waters and despite establishing improved correction methods, uncertainty remained for complex waters with extremely high scattering coefficients. Until an instrument with sufficient dynamic range becomes available that is suitable for highly turbid and clear oceanic waters, a methodology is required for measuring extreme backscattering using the existing instrumentation.
The magnitude of b bp has been shown to decrease linearly with decreasing particle concentrations (Boss et al. 2009;Neukermans et al. 2012). Thus, it is expected that serial dilution can be used to predict b bp when instrument saturation is observed. However, sample dilution may induce coagulation and flocculation, particularly if the salinity or pH is altered in the process (Goldberg and Glaubig 1987). Such effects may alter the particle size distribution (PSD) and consequently the predicted b bp (Mobley 1994;Morel 1974;Bohren and Huffman 2008). To monitor for these changes in a dilution series, Slade and Boss (2015) demonstrated a relationship between the backscattering spectral slope (γb bp ) and the average particle size, rather than the particle concentration.
The effect of chemical changes, settling, particle loss, and any other phenomena induced by the dilution process on predicted b bp can be examined by an analysis of the accuracy and precision of a dilution series. Particle assemblages containing coagulating particles are likely to undergo larger changes in their PSD across a series of dilutions due to their tendency to cluster when interacting with water (Tansel and Boglaienko 2019). Consequently, coagulating particles are also likely to have a greater impact on the accuracy and precision of the dilution method. Natural waters that saturate the ECO BB9 may contain a variety of constituents where a range of particle interactions could occur through dilutions to impact the methods performance. If data obtained with the dilution method is not assessed for the influence of PSD change on the b bp , this could result in inaccurate characterisations of b bp .
A literature review indicated few attempts to overcome instrument saturation in the field, the only published procedure to overcome the problems of saturation with standard backscattering instruments is that of Wong et al. (2020). Their method relies on measuring the nephelometric turbidity units (NTU) of an undiluted in situ sample, followed by measuring the NTU and backscattering of a series of dilutions of the sample such that the scattering is less than saturation. Wong et al. (2020) demonstrated that estimation of b bp from NTU worked well with powdered calcium carbonate, and in extremely turbid coastal water from the Singapore Straits (340 NTU) and Lupar River (360 NTU). Given the complexity of waters where instrument saturation is encountered, we test the performance of dilutions using synthetic and natural waters to determine its effectiveness in a range of settings. Specifically, we look for any dilution induced phenomena, to quantify its effects on the predicted b bp thereby determining the efficacy for any method which uses dilutions to determine b bp in freshwaters that saturate the ECO BB9.
In this paper we demonstrate the use of serial dilutions to determine b bp . We evaluate the accuracy, precision, and γb bp constancy with inland waters which commonly contain clay, CDOM, algal particulates, leaf litter, and ash from wildfires that come in through Australian catchments. These assessments demonstrate the efficacy of this approach in freshwater and tests whether obtaining b bp via dilution generates errors greater than the instrument uncertainty.

Dilution protocol
To carry out each serial dilution a 11 L matte black bucket was filled with 9 L of sample water, the BB9 was fastened into a bracket and held in place by retort stands (Fig. 1) was positioned with at least 5 cm between the sensors and the bucket walls to avoid measurement interference. This was determined to be sufficient given the instrument pathlength of 0.023 m (Vadakke-Chanat et al. 2018) and by observing the response of the sensors while varying the position of the instrument in the bucket with MilliQ. The bucket was covered with a black plastic bag to prevent incident light entering the measuring volume. Before each measurement, the sample was gently mixed to maintain particulate suspension, taking care to avoid the formation of bubbles.
Samples were diluted systematically by removing a known volume of solution and adding the same volume of 18 MΩ MilliQ keeping the sample volume constant. Dilutions were repeated until three to five measurements were made without any saturated wavelengths. Each backscattering measurement ran for 1-2 min with visual examination for signs of particulate settling. The measured b bp were checked for indications of particulate settling, saturation, and bucket interference and discarded as appropriate. A spirit level was used to ensure the instrument is oriented orthogonal to the surface of the water sample.
A preliminary evaluation of the method indicated that the dilution concentrations should commence at the point where all wavelengths are just unsaturated (C us ), then diluted further in subsequent equal steps as fraction of the unsaturated concentration as per Eq. 1. Where C is the desired concentration for a dilution step number (n) and N is the total number of dilution steps.
For example, if the original sample does not saturate the sensor and several measurements are made, one would take ECO BB9 measurements at 100%, 75%, 50%, and 25% of the original sample. If the sensor is unsaturated with a solution 75% of the original sample (C us = 75%), ECO BB9 measurements would be at 75%, 56.25%, 37.5%, and 18.75% of the sample. This ensures the concentrations being measured for the dilution regression change in a uniform manner relative to the total content in the original sample.

Sample characterization
Chlorophyll a The Inland Water Quality (IWQual) field work undertaken in Australian waterbodies during 2019-2022, measured chlorophyll a (Chl a) by collection of surface samples ($ 15 cm) in 5 L HDPE container following standard protocols (IOCCG 2000). The HPLC method described in Clementson (2013) was used to obtain the concentration of Chl a. Samples were prepared by vacuum filtering through Whatman glass microfiber filters, Grade GF/F, 0.7 μm. The volume of sample filtered for Chl a analysis was dependent on the concentration and type of particulates in the sample. Filters were immediately preserved in liquid nitrogen for transportation to the analytic facility.

Total suspended solids
The concentrations of total suspended solids (TSS) were determined by filtration of a known volume through preweighed glass fiber filters (Whatman GF/F). The filters were dried at 60 C and weighed to derive the TSS concentrations. The inorganic and organic fractions were then determined by difference after combustion of the organic component to CO 2 .

Particle size distribution
For synthetic waters, the particles from the 100% concentrations of three trials (Table 2) were measured in addition to the lowest concentration for each dilution series. This offered a method to observe induced flocculation or dispersion, and to provide an independent check on the extrapolated dilution results.
The PSD were measured by laser particle size analysis using a Malvern Mastersizer 3000 according to the manufacturer's operating instructions and with Mie theory for the evaluation setting. Deionized water was used as a control. The samples were then degassed, mixed, and sonicated at 100% power for 30 s in the wet cell before measurement of laser diffraction using 63 red or blue laser detectors positioned at different angles from the incident light source. Three replicate measurements were made for each sample and the mean PSD reported on a spherical particle volume basis. A measurement duplicate was performed on one of the seven samples as a check on analytical precision by repeating the process of filling the wet cell and again performing the measurement.
The percentage of particles below each diameter (range 0.01-2500 μm) was subtracted from each diameter step to determine the percentage of particles at each diameter. Changes to the PSD during dilutions were monitored by subtracting the PSD at the last dilution step from the PSD of the full sample concentration.

Sample collection
The dilution method was evaluated with natural and synthetic water samples. Natural samples were collected at six water bodies (Table 1). Synthetic samples were prepared by suspending finely ground Kaolinite in MilliQ water with optically active constituents to represent certain water types (Table 2). These included tea extracts to mimic CDOM absorption, spirulina from a live culture to simulate fine algal content, and ash from a wood fire to simulate runoff from wildfire affected catchments.

Natural waters
Dilution series were conducted on surface water ($ 15 cm) collected from multiple freshwater bodies in South East Australia in 2020-2021 (Fig. 2). The sites were Lake Burrinjuck, Lake Burley Griffin, Lake Bonney, Wachtel's Lagoon, Lake Victoria, Lake Pamamaroo, and water from the Darling River (Table 1). These sites were visited for the Australian Aquatic Bio-optical Dataset with Applications for Satellite Calibration, Algorithm Development, and Validation (Botha et al. 2020;Anstee et al. 2022). Additional parameters, including Chl a concentration, absorption, and apparent optical properties were measured as part of the field campaign (Anstee et al. 2022). Many of the sites visited for the Australian Aquatic Bio-optical Dataset affected by the wildfires in 2019-2020, which devastated many large catchments in South East Australia, hence, wood ash was a commonly encountered optically active constituent in waters draining these areas. The frequent occurrence of wood ash in this field work necessitated its inclusion in the experimentation for this dilution method.
At each site 20-40 L of water was collected in HDPE containers from the surface ($ 15 cm) to carry out serial dilutions within 12 h of collection. Care was taken to avoid direct solar heating of the samples in transit. Three approaches were used to evaluate the method's performance on these samples based on the circumstances encountered in the field. First, at those sites which saturated in situ, a single dilution series with evaluation of γb bp was the only way to parametrise the scattering properties in these conditions. Second, serial dilutions were carried out for natural waters that did not saturate the instrument. These were able to indicate accuracy of the method by comparison to the in situ measurement. Finally, when practicable, repeats of this method were carried out on waters from the same site to demonstrate precision. Time and MilliQ constraints in the field sometimes limited the extent of the latter.   Then algae were collected and added by: • Live spirulina particles from culture were filtered onto a 0.4 μm filter.
• MilliQ rinsed by a backflushing method, to be re-resuspended in MilliQ.
• The solution was left for 3 h to settle.
• The surface water was collected where the algae were floating (removing large > 0.4 μm sinking particles).
Note, while effort was made to separate most contents from the algal growth culture from the algae, there will be some unknown trace contaminants of which parameterisation was beyond this experiment's scope. PHY Inorganic particles with CDOM and algae (live spirulina) • 5 L of the 1.2 g L À1 kaolinite MilliQ concentrate mixed in 34 L of MilliQ (same base solution as FNAP). • Then eight English breakfast and two green tea bags were left soaking for 10 min in 1 L MilliQ. • The MilliQ was filtered through 0.2 μm pore size filter to remove fine organic particles that may have passed through the tea bags (same base solution as CDOM).
Then algae were collected and added by: • Live spirulina particles from culture were filtered onto a 0.4 μm filter.
• MilliQ rinsed by a backflushing method, to be re-resuspended in MilliQ, • The solution was left for 3 h to settle • The surface water was collected where the algae were floating (removing large > 0.4 μm sinking particles).
Note, while effort was made to separate most contents from the algal growth culture from the algae, there will be some unknown trace contaminants of which parameterisation was beyond this experiment's scope. ASH+ Inorganic particles with CDOM, fine organic particles, and ash • 22 L MilliQ.
• Eight English breakfast and two green tea bags were left soaking for 10 min in the kaolinite MilliQ solution. • 1.54 g wood ash.
The amount of kaolinite concentrate was decreased to prevent saturation of the sensor after ash was added.

Synthetic waters
Synthetic waters were constructed to test the method with stepwise addition of individual optically active constituents (non-algal particulates [NAP], CDOM, and phytoplankton) commonly estimated by remote sensing for water quality assessment (Ritchie et al. 2003). The constituents used were chosen with special consideration of components commonly encountered in Australian inland waters. The trial constituents included fine NAP (FNAP), CDOM, fine leaf litter (+), algal particulates (PHY), and wood ash (ASH).
Dilution trials were conducted in two rounds: FNAP1, CDOM+, PHY+, and ASH+ (Table 2), where the addition of unfiltered tea was used to simulate fine leaf litter with CDOM, signified with a "+". The second set of trials, FNAP, CDOM, PHY, and ASH (Table 2), introduced the step of filtering the tea through a 0.2 μm Pall Acropak capsule filter prior to inclusion to the trial solution. The filtering ensured small organic particles were excluded from the "CDOM" representative. The second set of trials were conducted with additional replicate dilutions for each water type and contained slightly higher concentrations of ingredients (Table 2). For each round of trials, the ingredients were added sequentially so that each trial tested a new constituent, comparable to others from the same round, with the ID specification defining the optically active constituents of interest as depicted in Fig. 3. The construction of each trial solution is specified in Table 2. A Kaolinite concentrate was prepared by grinding a commercially available Kaolinite, mined near Lake Pamamaroo, in a Tungsten Carbide puck mill and then mixing 24 g into 20 L of 18 MΩ MilliQ. The fine particles in this suspension were collected by allowing the concentrate to settle over 70 h then siphoning water from the top. This fine particle suspension was used in the trial solutions.
Measurements of TSS were collected for the full concentration of all the synthetic water trials. PSD was obtained for the full concentration and the most dilute concentrations of FNAP, PHY, and ASH. PSD of the CDOM trial was not obtained as scattering from CDOM is expected to be negligible. • Then eight English breakfast and two green tea bags were left soaking for 10 min in 1 L MilliQ. • The MilliQ was filtered through 0.2 μm pore size filter to remove fine organic particles that may have passed through the tea bags. 2.6 g wood ash.
The amount of MilliQ increased and kaolinite decreased to prevent saturation of the sensor after ash was added.

Absorption corrections
The ECO BB9 measures the volume scattering coefficient (β[θ,λ]) at nine wavelengths at 124 (units m À1 sr À1 ), where θ represents the measurement angle, and λ the wavelength (Doxaran et al. 2016). The β(θ,λ) were then corrected for the absorption (a t ) in the incident beam of light with Eq. 2a to yield the absorption corrected volume scattering (WETLabs 2007), where the instrument pathlength is 0.023 m (Vadakke-Chanat et al. 2018). Further corrections are made to remove the contribution of scattering from water (Eq. 2b). To derive b bp , the absorption corrected particulate scattering coefficient was converted to particulate backscattering via Eq. 2c.
The highest measurable b bp at each wavelength where saturation occurs, is dependent on the wavelength, specific calibration of the ECO BB9, and the absorption of the water. The highest and lowest absorption corrections from the IWQual dataset (Anstee et al. 2022) applied to the max raw ECO BB9 values, corrected as per Eq. 2 is shown in Fig. 4. This demonstrates the specific range of maximum b bp for each wavelength of the ECO BB9 used in this research.
To apply the absorption corrections (Eq. 2a) for each wavelength at each concentration measured in the ECO BB9 dilution protocol, the experimental trials on synthetic waters used coincident absorption measurements from a Seabird hyperspectral absorption and attenuation meter (AC-S). The AC-S uses two 10 cm pathlengths to acquire absorption and attenuation data in 81 channels with a bandwidth of 4 nm over 400-730 nm. The absorption values were corrected for salinity and temperature as in the ACS user manual (SeaBird 2013) then applied to ECO BB9 data (Eq. 2a). To determine absorption corrections for all ECO BB9 wavelengths at each dilution concentration, absorption models were derived for each trial. The absorption models came from linear interpolation of the absorption measured over a range of concentrations.
Absorption corrected ECO BB9 data was then processed by performing a linear regression on the median particulate backscattering at all dilution steps and then extrapolating to 100% to predict the (undiluted) sample b bp for each wavelength (λ). A control measurement of 18 MΩ MilliQ water was included as the zero concentration for each regression.

Evaluation of dilution method
The performance of the dilution method was evaluated by three methods: assessment of the accuracy of predicted b bp , assessment of the precision of the predicted b bp , and by monitoring for indications of changes in PSD between steps of a dilution series through the constancy of γb bp .

Accuracy
For samples that were less than the saturation limit of the ECO BB9, the dilution method accuracy could be evaluated through comparison of the mean predicted 100% b bp λ (P i ) from the dilution regression and mean measured 100% b bp λ m À1 (M i ) of each sample. Accuracy evaluation included assessments by the coefficient of determination (R 2 ), RMSE, MAPE, MAE, and bias. RMSE is the root mean squared error, MAPE is the median absolute percentage error, MAE is the mean absolute error (Pahlevan et al. 2020).

RMSE
Bias Levene's test (Levene 1960) is used to compare variance of trials RMSE with a significance level of 0.05. A two-sample t-test was then used to infer if changes observed in PSD are significantly impacting the method accuracy through comparison to the RMSE of a sample which demonstrated no dilution induced change in PSD.

Precision
For samples that were repeatedly measured using the dilution series method, the precision of the method was assessed via relative standard deviation, RSD (%), between the mean predicted b bp (M i ) and the standard deviation (σ) of predicted b bp (Eq. 7). Precision evaluation was carried out on samples in the measurable range of the ECO BB9 and on those that saturated it.
PSD change indicators within a series For all samples, the backscattering spectral slope (γb bp ) at 555 nm (Eq. 8) was calculated at each dilution increment. γb bp is related to the average PSD (Slade and Boss 2015), rather than concentration. As a result, evaluation of the variance of γb bp within a series was used to monitor the constancy of the PSD between dilution stages. The relative standard deviation of γb bp (γb bp RSD (%)), in Eq. 9, demonstrates the variation of PSD between dilution increments where σ is the standard deviation of γb bp and γb bpi is the series mean γb bp .
PSD change indicators from γb bp RSD (%) in conjunction with evaluation of the precision, RSD (%), offers capability to evaluate the performance of the method on samples that saturated the sensor in situ whereby an in situ measured value could not be obtained for accuracy evaluation (Eqs. 3-6).

Assessment
Overall dilution performance

Accuracy
The dilution method was able to accurately determine b bp in 413 instances of measured and predicted b bp from synthetic and natural waters (Fig. 5). The approach using Eqs. 3-6 demonstrated that the dilution method can provide reasonable estimates of b bp , with strong linearity, R 2 of 0.98, and RMSE of 0.031 (m À1 ) ( Table 3). This covers all nine wavelengths of the ECO BB9. Figure 5 suggests that the accuracy declines somewhat for the shorter wavelengths (412, 440, and 488 nm). However, the quantitative assessment (Table 3) shows that this is not the case, the higher error is predominantly due to one sample with 15.3 mg L À1 total TSS and 45.7% organic contents as revealed in Fig. 6a,c. Figure 6 reinforces the point that the deviations impacting on overall accuracy are independent of wavelength (Fig. 6a), TSS mg L À1 (Fig. 6b), and the percentage of organic TSS in the samples (Fig. 6c). Additional accuracy evaluations of b bp in the upper limits of the ECO BB9 measurable range (0.6-2.066602 m À1 ) from a more diverse range of sample types would improve the understanding of the method's performance. However, we can conclude that the simple dilution method approach will provide good estimates of b bp in a wide range of water types.

Precision
Repeated dilutions of synthetic and natural water samples exhibited high precision (Eq. 7) with only 1.87% of the b bp from nine wavelengths above 10% RSD for predictions up to 5 (m À1 ) which is 2.5 times the limit of the ECO BB9 (Fig. 7). Comparison of the RSD with the samples mean predicted b bp in Fig. 7 demonstrates that b bp precision holds with measurements beyond the measurable range of the ECO BB9. Inclusion of the sample properties in Fig. 7 reveals all the high b bp (> 1.2 m À1 ) evaluated here are attributable to just one sample type with low (%) organics. However, Fig. 7 also demonstrates that the precision of the overall dilution method was independent of the organic content in the samples (Fig. 7). Therefore, we expect precision to hold with samples of higher organic content beyond the measurable range of the ECO BB9. That said, specific particle types demonstrate greater impact on the method performance such as, the sample attribute to $ 32% organic TSS in Fig. 7 For this reason, repeat dilutions (three or more series on the same sample) with precision evaluation of b bp would be advised in practice to ensure the sample constituents are suitable for the dilution method and to explore further the boundaries of the dilution method.

PSD change indicators within a series
The γb bp RSD (%) (Eq. 9) demonstrates constancy of γb bp within a dilution series was also independent of the sample's TSS mg L À1 and organic content (Fig. 8). In Fig. 8, 78.8% of the dilution series exhibited γb bp RSD less than 10% of its series mean γb bp .

Sample characterization
The composition of the natural water samples used in the examination of the dilution method varied widely: in natural waters Chl a concentrations ranged from 8 to 43.2 μg L À1 (Fig. 9), TSS varied from 5 to 140 mg L À1 , and organic content was up to 80% of the TSS (Fig. 10). The lab constructed trials tested the method on samples with 26-65 mg L À1 TSS, with up to 45% organic TSS. There were no water samples in the range 75-110 mg L À1 total TSS and few samples that were over 50% organic content (Fig. 10).
The PSD results confirmed that there were minimal changes to synthetic samples made from Kaolinite and MilliQ prior to the inclusion of other constituents (Fig. 11). The difference between the dilute and undilute percentage of particles at each diameter step were close to 0% for all of FNAP (Fig. 11). There were some coagulations in the algae containing trial, PHY, with $ 13% more particles between 1200 and 1600 μm  after dilution and $ 3% less particles between 100 and 120 μm (Fig. 11). PHY had 0.12% and 3.19% particles beyond the PSD range (above 2500 μm) for the undiluted and diluted samples, respectively (Fig. 11). The samples containing wood ash (ASH) also had some coagulation, demonstrated by a loss of smaller particles ($ 0.15 μm) and an increase in larger particles ($ 100 μm) after dilution (Fig. 11). Note, the samples for PSD were preserved by refrigeration and limited light exposure, however, as PHY contained live algae, the sample itself could have changed slightly between the time the dilution ECO BB9 measurements were carried out and when the sample was analyzed for PSD.

Dilutions of natural waters
Seven field samples (Table 1) were in range of the ECO BB9 and therefore met the conditions for accuracy evaluation as per Eq. 3. Measurements from two sites (S1 and S3) used the in situ b bp as M i in Eq. 3. Hence, S1 and S3 are directly compared with the in situ environmental backscattering coefficient. Four sites had repeated dilutions carried out on them and therefore could be used for precision analyses as per Eq. 7. Closer inspection found that the sample decreasing both in accuracy and precision of the dilution method was S6 from Table 1 (Fig. 12a,c). This is expected to be the impact of a specific particle type because we have demonstrated dilution performance to be independent of the samples TSS and the organic fraction therein. The average γb bp RSD was 0.86% for S6 (Fig. 12c), indicating minimal changes in PSD between dilution steps within a singular series for S6 relative to other sites with better accuracy. S6 contained the highest concentration of Chl a (Fig. 9) with 26.4 μg L À1 greater than S7 which was from the same waterbody. This waterbody was noted to contain a large clump-forming species of algae (Table 1).

Dilutions of synthetic waters
Eight synthetic water samples (Table 2) were used for the dilution method, all of these could undergo accuracy tests as per Eq. 3 and precision tests as per Eq. 7. Inspection of each sample's performance (Fig. 13) demonstrated that the fine leaf litter from CDOM+ and to some extent PHY+ and ASH+ contributed to the tendency for error to increase at wavelength 440 nm (Fig. 13).
The sample with the largest impact on the precision of b bp predictions was from ASH (in Fig. 13b). ASH had accuracy like that observed in other trials (Fig. 13) which suggests there were changes of PSD between repeated dilutions impacting on the precision (Fig. 13). Increased effort in mixing of the original trial solution prior to each repeat dilution should help to minimize this type of influence on the precision evaluation.
The γb bp RSD (%) in the synthetic waters was greatest in CDOM+, ASH+, PHY, and ASH (Fig. 13c). This indicates that these trials had some dilution induced phenomena, such as coagulation, to change the sample composition within a dilution series. Figure 11 confirmed PSD changes in ASH and PHY  and that there were almost no changes in FNAP. Thus, comparisons of RMSE from ASH and PHY against the RMSE of FNAP is used to infer if the observed changes in PSD were drastic enough to significantly influence the methods accuracy. The RMSE of ASH had no significant difference (t-statistic: 1.8881, p value 0.0772) with FNAP and the RMSE for PHY was significantly lower than FNAP (t-statistic: À2.6753, p value 0.0166). Therefore, while there were PSD changes in ASH and PHY, this did not lead to a significantly higher RSME. In addition, there were no changes in γb bp with the extent of dilution for each of these trials, on account of the R 2 for PHY being 0.46 and the R 2 for ASH being 0.43. Given the association between γb bp and the average particle size, this is consistent with the conclusion that the observed changes in PSD did not significantly affect the b bp values obtained using this method. If the γb bp RSD (%) from a dilution series is equal to or less than that observed here, for freshwater samples diluted according to the method, similar or better prediction accuracy is anticipated.

Absorption corrections
For trials with coincident measurements of absorption at two or more concentrations in the dilution series, the absorption correction values were derived from a regression of the measured absorptions and their concentrations. The validity of using this approach to derive absorption correction factors at any concentration was confirmed through analysis of the R 2 , gradient, and intercept displayed in Fig. 14. For all the trials where regression was carried out, the R 2 of the absorption regressions were above 0.9 for all the wavelengths of interest (410-715 nm). The gradient of all the regressions at every wavelength were about 100 times smaller than the actual 100% absorption curves. All the intercepts (except PHY+) were 0 or close to 0 indicating that, in most circumstances, absorption decreased linearly with concentration. The success of the absorption regression (Fig. 14) established assumptions that could be applied to trials with only one absorption measurement at 100%, such as trials FNAP1, ASH+.

Discussion
The dilution method described here enables spectral characterization of b bp from water types that have previously been excluded from research because of instrumentation   The method is a reliable and effective way to derive b bp because the uncertainty of the dilution method is comparable to acceptable uncertainty of remote sensing retrieval of backscattering (Brando et al. 2012;Bisson et al. 2021). Comparisons between measured and predicted b bp demonstrated that the dilution method has high accuracy with an R 2 of 0.98, MAPE 5.348%, and RMSE of 0.031 (m À1 ). This uncertainty was higher compared to the uncertainty of "typical" field measurements without dilution (in waters where instrumentation saturation did not occur), with the instrument's highest error of 6.21EÀ05 m À1 sr À1 at wavelength 412 nm. Thereby imposing the need to quantify dilution induced error in practice to define the known uncertainties of the measurement approach (Werdell et al. 2018).  The accuracy and precision of the dilution method were in the same range for both natural waters and the synthetic waters, with the "spikes" attributable to the specific contents of some samples such as large algae species (S6), Ash (ASH), and fine plant debris (CDOM+, PHY+, ASH+). For this reason, use of dilutions for b bp characterization should undergo repeated dilutions to quantify the precision for a given water type in conjunction with the method's in-built quality control of γb bp constancy analysis.
Future studies in optically complex waters with repeated serial dilutions, γb bp evaluation, and PSD analysis will provide the opportunity to further extend the method with a range of constituents and salinities. Specific areas for investigation include: the impact of large algae species, and the response of PSD and γb bp with the extent of dilution and flocculation. This information will better define any limits within which the method can be used. The greatest impact on the dilution uncertainty here is due to a large clump-forming species of algae that was observed in the water of S6. Extreme waters containing algal blooms have demonstrated sensor saturation and demonstrated the need for development of new approaches (Moore et al. 2017). Given the limited use of water samples containing algae in this study, further exploration of the dilution method and its precision in turbid waters with algae identification is recommended. This will not only further establish conditions of the method efficacy, but it will also expose the ways in which different morphological features and biological characteristics influence b bp within complex turbid waterbodies.
Natural blooms have significant and unique contributions to particulate scattering where small phytoplankton particles have a wavelength-specific backscatter response, with higher backscatter in the blue, while larger particles backscatter light similarly at all wavelengths (Soja-Woźniak et al. 2020). b bp are influenced by the cellular particulate organic carbon content and cell size of algae species (Zhou et al. 2012). The error from the algae containing synthetic water sample, PHY, did not increase like that of S6 thereby demonstrating species dependent impacts on the method. The b bp of some species such as Microcystis aeruginosa are not well predicted through Mie Theory (Zhou et al. 2012). Due to colony interactions in situ, such species exhibit different backscattering responses from both the modeled and measured single cell (Moore et al. 2017). These species dependent and complex interactions highlight clear requirements for in situ characterization of turbid waterbodies with high algal content (Soja-Wozniak et al. 2019).
Increased knowledge of the b bp of specific contents and particle assemblages in highly turbid waters will advance remote sensing products which depend upon the scattering for optical water type classifications. Climate change produces an increased intensity of wildfires and rainfall events leading to an increased need to quantify highly turbid runoff including pyrogenic materials in water systems. Therefore, the inclusion of pyrogenic materials in aquatic optics research is crucial for the development of remote sensing products. Improvement of such products will increase the capability of surface water quality monitoring to inform management decisions, particularly in areas which are not easily accessible.
Surface water is an important global resource and plays a fundamental role in biogeochemical cycling, maintenance of biodiversity, human wellbeing, and prosperity (Tyler et al. 2016;Spyrakos et al. 2018). Improving natural resource management and protecting and restoring aquatic ecosystems was identified as a key priority for the UN Sustainable Development Goals (SDG), particularly SDG 6 (clean water and sanitation) and SDG 14 (Life below water). It requires the implementation of integrated water resources management systems, often supplemented by the application of satellitederived water quality assessment. The retrieval accuracy of remote sensing algorithms is underpinned by the precision of in situ IOP measurements, including the correct b bp characterization of optically complex water bodies.

Comments and recommendations
It is recommended to carry out repeat dilutions on the same sample to quantify the precision and uncertainties. This, in conjunction with evaluation of morphology of algae and sediment impacting b bp will help further resolve the method's performance in the presence of specific constituents. This applies particularly to waters with constituents that were not tested in this study such as coastal or marine waters.
Evaluation of the constancy of γb bp across dilution steps offers an in-built quality control to indicate if there have been drastic PSD changes between dilution steps. If there are signs of PSD change, γb bp RSD, greater than exhibited by synthetic waters here, further analysis into the degree to which the method's performance is impacted would be necessary.
In coastal waters, filtered seawater may need to be used in place of MilliQ. Maintaining ionic stability during dilution is important to prevent coagulation and dispersion. The applicability of this suggested approach is unknown as it has not been tested in this study.
Although efficacy of the dilution method has been demonstrated, the requirement for copious amounts MilliQ water in the field is often not feasible, thus limiting the samples that can undergo dilutions. A dilution performance evaluation in conjunction with the NTU based prediction of b bp demonstrated by Wong et al. (2020) offers more practicality for b bp measurement where MilliQ resources are scarce or for water column profiles of saturating natural waterbodies.
This study's dilution method, by itself or together with the method of Wong et al. (2020), offers a solution to specific IOP characterization for freshwaters with turbidity outside the measurable range of the ECO BB9. Implementation of this method globally with published results will specify the b bp ranges (and signal to noise requirements) for an instrument capable of measuring complex water.
We now have data beyond the measurable range of the ECO BB9 for complex inland waters, the availability of this data will advance research in remote sensing and bio-optical algorithm to improve water quality monitoring applications in line with UN Sustainable Development Goals.

Data Availability Statement
Data and metadata are available at https://data.csiro.au/ collection/csiro:58079