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Effect of Water Temperature and Salinity on the Jet Erosion Test (JET) Discharge Coefficient
Joanna Quiah1, Celso Castro-Bolinaga1,*, Steven G. Hall1, Garey A. Fox1, Nina Stark2
Published in Journal of Natural Resources and Agricultural Ecosystems 2(1): 29-37 (doi: 10.13031/jnrae.15337). Copyright 2024 American Society of Agricultural and Biological Engineers.
1 Biological & Agricultural Engineering, North Carolina State University, Raleigh, North Carolina, USA.
2 Engineering School of Sustainable Infrastructure and Environment, University of Florida, Gainesville, Florida, USA.
* Correspondence: cfcastro@ncsu.edu
The authors have paid for open access for this article. This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License https://creative commons.org/licenses/by-nc-nd/4.0/
Submitted for review on 1 September 2022 as manuscript number NRES 15337; approved for publication as a Research Brief by Associate Editor Dr. Meetpal Kukal and Community Editor Dr. Kati Migliaccio of the Natural Resources & Environmental Systems Community of ASABE on 22 August 2023.
Highlights
Abstract. The discharge coefficient (Cd) of the Jet Erosion Test (JET) directly affects the calculation of applied shear stresses (to) during testing and, therefore, of JET-derived erodibility parameters, namely, the soil’s critical shear stress (tc) and erodibility coefficient (kd). Typically, Cd is assumed to be constant for a given combination of JET device (e.g., original vs. mini) and setup (e.g., head tank vs. pressure gage), disregarding the effects of varying environmental conditions. The objective of this study was to quantify the impact of changing water temperature and salinity on the Cd of a mini-JET device fed by a pressure head tank. Laboratory experiments were conducted to determine the variability in Cd for ranges of water temperature between 10 and 30°C and salinity between 0 and 35 ppt. Results showed that Cd was sensitive to changes in both variables, with water temperature generating a more significant impact. Cd was negatively correlated to water temperature, decreasing by as much as 20% when temperature increased from 10 to 20°C, and positively correlated to salinity, increasing at low levels but remaining relatively constant for levels greater than 5 ppt. When extrapolated to erosion curves and JET-derived erodibility parameters, the variability in Cd significantly impacted the calculation of to and the magnitude of tc and kd, highlighting the degree of uncertainty that could be associated with these variables because of an uncalibrated Cd. Lastly, results from the laboratory experiments were used to develop a normalized predictive model and associated curves for application to other mini-JET devices with similar setups.
There is a growing need for developing an improved understanding of erosion phenomena and mitigation strategies in fluvial and coastal environments (Fox, 2019; Tullos et al., 2021; NOAA, 2022). Soil erodibility is typically thought to be a function of applied stress and soil properties, but it may also be affected by environmental variables such as water temperature and salinity (e.g., Olson, 2019; Rajesh and Rehana, 2022). Hoomehr et al. (2018) showed that erosion rates can increase by as much as a factor of eight with increasing water temperature, with the effects of salt concentration constrained by water pH. Likewise, Akinola et al. (2019) found that erosion rates can vary significantly depending on the difference between soil and water temperatures, with larger differences resulting in increased erosion rates.
A commonly used approach to quantifying soil erodibility is the Jet Erosion Test (JET) (Hanson 1990, 1991; Fox et al., 2022). The JET allows for in-situ determination of erodibility parameters, namely, the soil’s critical shear stress (tc) and erodibility coefficient (kd) (Fox et al., 2022). These parameters depend on the measured relationship between applied shear stresses (to) and erosion rates (er) during testing, as given by the excess shear stress equation (Partheniades, 1965):
(1)
where a is a positive numerical exponent often assumed to be unity (Wahl, 2021). Therein:
(2)
where
Cf = 0.00416 = the coefficient of friction
? = water density
= the velocity of the water jet at the nozzle
Cd = discharge coefficient
g = gravitational acceleration
h = pressure head
Jp = Cdo = the potential core length
C = 6.3 = the diffusion coefficient
do = nozzle diameter
J = measured scour depth.
From these variables, ? and Cd will be impacted by varying water temperature and salinity. While ? can be readily adjusted to account for variations, Cd is a calibration parameter considered to remain constant for a given combination of JET device (e.g., original [Hanson and Cook, 2004] vs. mini [Al-Madhhachi et al., 2013]) and setup (e.g., head tank [Wardinski et al., 2018] vs. pressure gage [Ursic and Langendoen, 2021]). In fact, it is standard operating practice to calibrate each JET device and setup because Cd will be specific to manufacturer’s quality as well as to geometrical characteristics like nozzle shape and length of water supply hoses.
Varying environmental conditions, however, will impact Cd as its magnitude reflects energy losses that occur as water travels from the source to the jet nozzle (e.g., Sabersky et al., 1999), which are in turn impacted by water properties (e.g., density and viscosity) that depend on temperature and salinity. The objective of this study was to quantify the effect of water temperature and salinity on Cd. These two variables were selected because they vary widely across fluvial and coastal environments (e.g., Olson, 2019; Rajesh and Rehana, 2022) and can significantly impact the soil’s erodibility behavior (e.g., Hoomehr et al., 2018; Akinola et al., 2019). A recirculating water system was designed and constructed to conduct laboratory experiments for calibrating the Cd of a mini-JET device fed by a pressure head tank over values of water temperatures and salinities that ranged between 10-30°C and 0-35 ppt, respectively. To demonstrate the impact on JET-derived erodibility parameters, the obtained variability of Cd was used to simulate changes in the relationship between er and to, and thereby in the magnitude of tc and kd, based on JET data collected by Wardinski et al. (2018). Lastly, results from the laboratory experiments were used to develop a predictive relationship that can be applied to estimate Cd based on a reference value and measured water temperature and salinity. Overall, this research brief contributes toward a more practical and consistent standard operating practice for the JET.
Materials and Methods
Mini-JET Device and Recirculating Water System
The laboratory experiments were conducted using a mini-JET device (fig. 1). The device has a nozzle diameter do = 3.18 mm, positioned in the center of an orifice plate with a diameter of 9.53 mm and a thickness of 4.83 mm. The orifice plate is located at the end of a pipe with the same diameter that is used to route water to the jet nozzle. Moreover, the device consists of a water inlet, jet valve, rotatable plate, submergence tank (height of 70 mm and diameter of 101.6 mm), foundation ring, water outlet, and point gauge. The device also has a digital pressure gage installed (0 to 200 psi; SSI Technologies, Inc.).
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| Figure 1. The mini-JET device. |
The mini-JET device was connected to a recirculating water system designed and constructed to minimize water losses (fig. 2). Water circulation was created using a ¼-hp submersible pump (Drummond) with 38.1-mm polyvinyl chloride (PVC) connectors, which were placed inside a 32-gallon plastic reservoir. The ¼-hp Drummond pump supplied water to the pressure head tank, which in turn provided water to the mini-JET device at a constant pressure head (h) via an ethylene vinyl acetate (EVA) hose with a diameter of 38.1 mm and a length of 5.9 m. A ball valve was installed above the pump to adjust the flow rate supplied to the head tank so that the tank would not overflow while recycling excess water back into the reservoir. Likewise, excess water from the pressure head tank was directed back to the reservoir to be recycled.
Laboratory Experiments with Variable Water Temperature and Salinity
Laboratory experiments were conducted for calibrating Cd over the selected range of water temperatures and salinities following the JET device calibration procedure outlined in the spreadsheet tool described in Daly et al. (2013). For each experiment, Cd was determined as the slope of the relationship between measured discharges through the jet nozzle (Qm) and their theoretical values (Qt) over a range of h (i.e., Cd = Qm/Qt). To compute Qm, water flowing freely through the jet nozzle was collected in a 1,000 mL graduated cylinder (fig. 2) while recording the time it took to fill 200-mL increments, considering a first trial the filling time from 0 to 200 mL, a second trial from 200 to 400 mL, and a third trial from 400 to 600 mL. Then, Qm was calculated by dividing the 200-mL volume by the corresponding filling time. From Bernoulli’s equation, it can be shown that Qt is given as follows (Sabersky et al., 1999):
(3)
where A = p(do/2)2 is the area of the jet nozzle. Equation 3 provides a theoretical value of discharge because energy losses are neglected in its derivation. Therefore, Cd captures the contribution of energy losses that occur as water travels from the head tank to the jet nozzle (fig. 2), which in turn depend on water properties like density and viscosity that vary with temperature and salinity. The laboratory experiments were conducted using a range of h that increased from 91.4 to 152.4 cm at 15.2-cm intervals. As shown in figure 2, h was measured from the top of the head tank to the location of the jet nozzle using an aluminum telescoping grade rod. Hence, values of Cd represent the performance not only of the main portions of the mini-JET device (e.g., orifice plate and nozzle), but also of other parts of the experimental setup that connect the head tank to the device (e.g., supply hose, elbows, and fittings). Importantly, values of Cd should reflect energy losses associated with the setup used to establish and measure the pressure head when running JETs (e.g., head tank vs. pressure gage), so that to can be calculated consistently. Limited guidance currently exists for setting these types of operational parameters (Fox et al., 2022). Lastly, an average Cd was determined for each experiment based on the three trials.
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| Figure 2. Schematic of recirculating water system designed and constructed to conduct the laboratory experiments for calibrating the mini-JET device’s Cd over a range of water temperatures and salinities. |
A total of 24 treatment levels consisting of variable water temperature and salinity were examined. To analyze the effects of salinity, Cd was determined at salinity increasing from 0 to 35 ppt at 5-ppt intervals, representing a range of typical values from freshwater (< 0.5 ppt) to seawater (33-38 ppt). Salinity was controlled with Instant Ocean Sea Salt (Instant Ocean, n.d.) (primarily NaCl), and monitored using a salinity refractometer (Wiztech Digital). Regarding temperature, Cd was determined at water temperatures of 10°C, 20°C, and 30°C. This range was guided by a large dataset of JETs performed on streambanks across the North Carolina Piedmont (Swanson and Castro-Bolinaga, 2022). Temperature was constantly monitored near the center of the reservoir using digital (YSI Incorporated) and glass thermometers. For the experiments with water at 10°C, the reservoir was initially placed in a cooler at 5°C and then progressively brought up to temperature before the start. Filtered ice was immediately added as needed when the temperature increased above 10°C. For the experiments with water at 20°C and 30°C, temperature was controlled by placing 150W glass insertion heaters (Aqueon Products) (fig. 2) in two separate reservoirs, one designated for each temperature. The heaters were left in the covered reservoirs overnight to ensure thorough heating. During the experiments, heat loss was prevented by keeping the opening of the reservoir covered as much as possible, which was achieved using a plastic lid and a blanket. Control readings of water temperature and salinity were taken immediately prior to and after each treatment level. The maximum variability recorded during the experiments for the target water temperatures was within ±1°C. The laboratory experiments were conducted sequentially for each water temperature, starting at 0 ppt and then increasing salinity levels by 5 ppt after completing the three trials. This approach was adopted because it took longer and required more effort to establish the target water temperatures (especially for 10°C and 30°C, as described before) than to establish well-mixed values of target salinities. The latter would typically take between 30 s and 2 min of adding salt, followed by an additional 2 min of stabilization and dissolving period for 30°C, 5 min for 20°C, and 10 min for 10°C. Lastly, before proceeding with different water temperatures, the recirculating water system was completely drained and flushed with freshwater.
Analysis of JET Data
It can be determined from equation 2 and the definition of 
that to is proportional to Cd2, implying that changes in Cd result in a quadratic response in to. To demonstrate the impact of changes in Cd on the relationship between er and to as well as on JET-derived erodibility parameters tc and kd, the variability in Cd obtained over the range of tested water temperatures and salinities was applied to JET data collected by Wardinski et al. (2018). Specifically, the obtained variability in Cd was used to simulate changes, first, in the relationship between er and to by adjusting to as a function of Cd via equation 2, and secondly, in the magnitude of tc and kd as calculated via the scour depth method by varying Cd within the spreadsheet developed by Daly et al. (2013). The Wardinski et al. JET data were selected because their experiments were performed with the same mini-JET device as used in this study, ensuring that the remaining device-dependent parameters that affect to in equation 2 did not change.
Results and Discussion
Variability of Cd with Water Temperature and Salinity
The laboratory experiments indicated that Cd varied with both water temperature and salinity (fig. 3). For 0 ppt, averaged values of Cd of 0.78, 0.64, and 0.60 were calculated at 10°C, 20°C, and 30°C, respectively. This represented a decrease of nearly 18% in Cd when water temperature increased from 10°C to 20°C, and a decrease of nearly 7% when temperature increased from 20°C to 30°C. When salinity was increased to 5 ppt, the average value of Cd increased by 7.9%, 2.4%, and 4.7% at 10°C, 20°C, and 30°C, respectively (fig. 4). However, such an increase in Cd was only observed with the initial introduction of salt. As salinity continued to increase from 5 to 35 ppt, Cd varied on average by 1.9%, 0.5%, and 1.6% at 10°C, 20°C, and 30°C, respectively. Overall, results suggested a significant dependence of Cd on water temperature. On average, across the range of tested salinities, Cd decreased by nearly 21% when the water temperature increased from 10°C to 20°C and by approximately 7% when the temperature increased from 20°C to 30°C.
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| Figure 3. Variability of Cd over the tested range of water temperatures and salinities. |
 |
| Figure 4. Percent change in Cd when compared to its value at 0 ppt over the tested range of water temperatures and salinities. |
The obtained variability in Cd was driven by changes in water properties that depend on temperature and salinity, specifically its density (?) and dynamic viscosity (µ), or equivalently, its kinematic viscosity (?), defined as ? = µ/?. On average, across the range of tested salinities, ? decreases by nearly 40% when temperature increases from 10°C to 30°C (e.g., for 0 ppt, ? decreases from 1.31×10-6 m2/s at 10°C to 8×10-7 m2/s at 30°C) (Sabersky et al., 1999; Sharqawy et al., 2010; Nayar et al., 2016). Changes in ? due to varying salinity are less significant for the tested water temperatures. From 0 ppt to 35 ppt, ? increases by nearly 5% at 10°C, and by approximately 6% at both 20°C and 30°C (Sabersky et al., 1999; Sharqawy et al., 2010; Nayar et al., 2016). Therefore, the obtained variability in Cd, which showed a stronger dependence on temperature, was consistent with changes in ? across the tested range of temperatures and salinities.
The obtained variability in Cd can be further evaluated as a function of the Reynolds number (Re), defined as Re = Utdo/?, where 
is the theoretical velocity of the water jet at the nozzle. As shown in figure 5, Cd decreased with increasing Re, driven by changes in ? over the tested range of water temperature and salinities. Such a relationship between Cd and Re is consistent with the well-established trend for the hydraulic performance of orifice plates (e.g., Streeter, 1958; Sabersky et al., 1999), suggesting that Cd was heavily impacted by energy losses caused by the reduction in diameter (from 9.53 mm to 3.18 mm) imposed by the orifice plate that encloses the jet nozzle (fig. 1). It should be noted that in this study, Cd represented more than the hydraulic performance of the main portions of the mini-JET device (e.g., orifice plate and nozzle). Cd also reflected the hydraulic performance of other parts of the experimental setup that connected the head tank to the device (e.g., supply hose, elbows, and fittings) (fig. 2), making it necessary to recalibrate its value for any changes in these parts of the experimental setup. For example, when using the digital pressure gage located near the mini-JET device’s orifice plate and nozzle to measure h, Wahl (2019) obtained Cd = 0.97, a value that is relatively high compared to those obtained herein (Cd-range = 0.59-0.86) or reported by others (Cd-range = 0.70-0.75) (Wahl, 2019). Wahl (2019) did not indicate the water temperature and salinity associated with the obtained Cd. These differences indicate that Cd for a given mini-JET device and setup is relevant only to the particular instrument setup. Additional work is needed to verify that the behavior of Cd obtained over the tested range of water temperatures and salinities (fig. 5) remains approximately the same if changes in the setup are made (e.g., length of the supply hose) or the digital pressure gage is used instead to measure the pressure head (e.g., Wahl, 2019).
 |
| Figure 5. Cd as a function of the Reynolds number (Re) over the tested range of water temperatures and salinities. |
Impacts on Erosion Curves and Derived Erodibility Parameters
A JET experiment conducted by Wardinski et al. (2018) on sandy loam soil (71.5% sand, 16% silt, 12.5% clay), referred to as SL-1, was selected to illustrate how the observed variability in Cd (as shown in fig. 3) influenced the relationship between er and to, as well as the magnitude of tc and kd. Wardinski et al. (2018) conducted their JETs with freshwater (< 0.5 ppt) at an ambient temperature of around 20°C. To demonstrate the impact of varying water temperature on the relationship between er and to, averaged values of Cd for 0 ppt salinity at 10°C (Cd = 0.78) and 30°C (Cd = 0.60) were used to simulate adjustments in the magnitude of to via equation 2. Likewise, to demonstrate the impact of varying salinity, to was adjusted using averaged values of Cd for 20°C water temperature at 0 ppt (Cd = 0.64) and at salinities = 5 ppt (Cd = 0.66). Results showed that differences in the relationship between er and to caused by varying water temperature and salinity were larger at higher to, with water temperature generating a greater change than salinity (fig. 6). For varying water temperature, the minimum and maximum absolute changes in to were approximately 1 Pa at low stresses and nearly 8 Pa at high stresses, respectively, with lower water temperatures resulting in larger values of to. In the case of varying salinity, the corresponding absolute changes were less than 0.3 Pa at low stresses and nearly 1 Pa at high stresses, with higher salinities resulting in larger values of to. These results were expected as to is proportional to Cd2 (eq. 2). Beyond the absolute changes illustrated in figure 6, which are specific to the SL-1 test conducted by Wardinski et al. (2018) and that will inherently vary when extrapolated to other soil materials, results showed that the obtained variability in Cd significantly impacted the calculated range of to. For varying water temperature, the calculated range of to increased by nearly 70% when water temperature varied from 30°C to 10°C, whereas the corresponding increase for varying salinity was only 6% for values = 5 ppt. Importantly, changes in the calculated range of to have implications when understanding soil erosion behavior as predicted by equation 1, in which such a range impacts the slope of the relationship if assuming linearity or the value of the positive numerical exponent a if assuming non-linear behavior (Wahl, 2021). The simulated adjustments in the magnitude of to highlighted the degree of uncertainty that could be associated with the relationship between er and to because of an uncalibrated Cd with regard to water temperature and salinity.
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| Figure 6. Changes in the relationship between er and to due to variations in Cd resulting from changes in water temperature (left) and salinity (right). Data correspond to test SL-1 conducted by Wardinski et al. (2018). |
To demonstrate the impact on JET-derived erodibility parameters, averaged values of Cd obtained for each treatment level (fig. 3) were applied to simulate adjustments in the magnitude of tc and kd using the scour depth method embedded within the spreadsheet developed by Daly et al. (2013). As expected, based on the obtained variability in Cd, results showed that both tc and kd were more sensitive to variations in water temperature than salinity, with lower temperatures generating a greater change. On average, across the range of tested salinities, tc decreased by approximately 1.2 Pa (37%) when water temperature increased from 10°C to 20°C, and by nearly 0.3 Pa (14%) when temperature increased from 20°C to 30°C (fig. 7). Moreover, tc increased with increasing salinity, with the largest variability occurring at 10°C (fig. 7). Regarding kd, it increased on average across the range of tested salinities by 42 cm3/N·s (59%) when water temperature increased from 10°C to 20°C, and by approximately 18 cm3/N·s (16%) when temperature increased from 20°C to 30°C (fig. 8). When compared to its range, the largest relative change in kd with salinity occurred at 10°C, with kd decreasing with increasing salinity over the range of tested temperatures (fig. 8). These results suggested that the impact of Cd on the erosion rate curves (fig. 6) translated into considerable changes in the magnitude of erodibility parameters, importantly generating a variation up to an order of magnitude in kd. Like the erosion rate curves, these results are specific to the SL-1 test conducted by Wardinski et al. (2018) and will inherently vary when extrapolated to other soil materials. Moreover, they are also specific to the scour depth method that was selected to solve for tc and kd and will vary if other methods are used (see Wahl (2021) for a comprehensive comparison of available methods). Nonetheless, results highlighted the variability that could be added to tc and kd because of an uncalibrated Cd with regard to water temperature and salinity.
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| Figure 7. Impact of Cd on tc over the tested range of water temperatures and salinities (left) and variability of tc with salinity at the tested water temperatures (right). In Cd vs. tc, salinity increases from left to right. |
Transferability To Other Mini-JET Devices with Similar Setups
While the obtained values of Cd (fig. 3) were specific to the mini-JET device and setup used in this study, its relative variability over the applied treatment levels reflected the impact of the tested range of water temperatures and salinities. A normalized quadratic model was developed in R software (R version 3.6.1, R Foundation for Statistical Computing) for adjusting Cd as a function of water temperature and salinity as:
(4)
  |
| Figure 8. Impact of Cd on kd over the tested range of water temperatures and salinities (left) and variability of kd with salinity at the tested water temperatures (right). In Cd vs. kd, salinity increases from left to right. |
where
Cd* = normalized discharge coefficient
Cd = predicted discharge coefficient adjusted for water temperature and/or salinity
Cd-f20 = calibrated coefficient using water at 0 ppt and 20°C
S = salinity in ppt
T = water temperature in °C.
Therefore, in order to apply equation 4, JET users must know Cd-f20 for their specific mini-JET device and setup. The predictive model was fitted to the obtained values of Cd (fig. 3), normalized by its averaged value at 0 ppt and 20°C (Cd = 0.64). The model consisted of linear and quadratic terms for water temperature, a linear term for salinity, and a term accounting for the interaction of both variables. The interaction term reflected that the extent to which salinity impacted Cd was affected by water temperature. The quantile-quantile plots indicated a normal distribution of residuals, with all but one term significant at level a = 0.05 (interaction term had a p-value of 0.06). Moreover, the model’s adjusted coefficient of determination (R2) was 0.95.
Using equation 4, curves showing the normalized variation of Cd over the tested range of water temperatures and salinities are shown in figure 9. Based on the JET users’ specific Cd-f20, these curves can be readily used to transfer results from this study to other mini-JET devices with similar setups (i.e., fed by a pressure tank using a relatively long supply hose) as follows: (1) determine Cd* for the target water temperature and/or salinity; and (2) calculate Cd as the product of Cd* and Cd-f20. It should be noted that the aim of equation 4 and figure 9 is to provide an estimate of the potential variability in Cd based on changes in water temperature and salinity. Ideally, Cd should be determined for each individual JET device and setup.
Conclusions
A series of laboratory experiments were conducted to quantify the variability in Cd of a mini-JET device. These experiments were conducted under varying water temperatures, ranging from 10 to 30°C, and salinities ranging from 0 to 35 ppt. The Cd values obtained from these experiments impacted the calculation of applied fluid forces and, consequently, the derivation of erodibility parameters. Results indicated that Cd was sensitive to variations in both water temperature and salinity, with the former variable generating a more significant impact. Regarding water temperature, Cd was negatively correlated to this variable, increasing its magnitude as temperature decreased, with larger changes associated with lower temperatures. In the case of salinity, low levels initially impacted Cd, but its magnitude remained relatively constant for levels greater than 5 ppt. When extrapolated to erosion curves, the obtained variability of Cd notably impacted the calculation of to at higher stresses. The changes in Cd also impacted the magnitude of JET-derived erodibility parameters, with tc increasing with increasing water temperature and salinity, and kd showing the opposite behavior. When considering their compounding effect, larger changes in tc and kd were associated with lower temperatures over the tested range of salinities. These findings showed that an uncalibrated Cd with regard to water temperature and salinity could lead to critically under- or overestimating a soil’s erosional behavior, highlighting the need to measure and report these variables when running JETs, particularly in natural streams where changes can occur daily and seasonally. Alternatively, the normalized predictive model and associated curves provided in this study offered an approach to transferring the obtained variability of Cd to other mini-JET devices with similar setups for adjusting Cd as a function of water temperature and salinity.
 |
| Figure 9. Normalized variability of Cd over the tested range of water temperatures and salinities. |
Acknowledgments
The authors acknowledge funding from the National Science Foundation (NSF) through grants CMMI-1820848 and CMMI-1820842. This work was also supported by the USDA National Institute of Food and Agriculture Hatch Project 1016113. Thank you to Melody Thomas and Alexis Swanson for assisting with assembling the recirculating water system and conducting the laboratory experiments. We also want to thank Neil Bain for his assistance with the construction of the experimental setup.
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