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Journal of Geophysical Research: Biogeosciences
RESEARCH ARTICLE On Factors Influencing Air-Water Gas Exchange 10.1002/2017JG004299 in Emergent Wetlands Key Points: David T. Ho1 , Victor C. Engel2 , Sara Ferrón1 , Benjamin Hickman1, Jay Choi3, and • Wind speed is not a good correlate for 3 gas exchange in emergent wetlands, Judson W. Harvey
and parameterizations developed for 1 2 3 lakes and the ocean are inappropriate Department of Oceanography, University of Hawaii, Honolulu, HI, USA, U.S. Forest Service, Fort Collins, CO, USA, U.S. • Rain contributes significantly to gas Geological Survey, Reston, VA, USA exchange in emergent wetlands • Gas exchange in emergent wetlands could be parameterized by rain rate, Abstract Knowledge of gas exchange in wetlands is important in order to determine fluxes of climatically water flow, and outgoing heat flux and biogeochemically important trace gases and to conduct mass balances for metabolism studies. Very few studies have been conducted to quantify gas transfer velocities in wetlands, and many wind speed/gas exchange parameterizations used in oceanographic or limnological settings are inappropriate under Correspondence to: conditions found in wetlands. Here six measurements of gas transfer velocities are made with SF6 tracer D. T. Ho, [email protected] release experiments in three different years in the Everglades, a subtropical peatland with surface water flowing through emergent vegetation. The experiments were conducted under different flow conditions and with different amounts of emergent vegetation to determine the influence of wind, rain, water flow, Citation: Ho, D. T., Engel, V. C., Ferrón, S., Hickman, waterside thermal convection, and vegetation on air-water gas exchange in wetlands. Measured gas transfer B., Choi, J., & Harvey, J. W. (2018). On velocities under the different conditions ranged from 1.1 cm h 1 during baseline conditions to 3.2 cm h 1 factors influencing air-water gas when rain and water flow rates were high. Commonly used wind speed/gas exchange relationships would exchange in emergent wetlands. Journal of Geophysical Research: overestimate the gas transfer velocity by a factor of 1.2 to 6.8. Gas exchange due to thermal convection Biogeosciences, 123, 178–192. https:// was relatively constant and accounted for 14 to 51% of the total measured gas exchange. Differences in rain doi.org/10.1002/2017JG004299 and water flow among the different years were responsible for the variability in gas exchange, with flow accounting for 37 to 77% of the gas exchange, and rain responsible for up to 40%. Received 10 NOV 2017 Accepted 19 DEC 2017 Accepted article online 4 JAN 2018 Published online 24 JAN 2018 1. Introduction Corrected 25 JAN 2019 Knowing the rate of gas fluxes in wetlands is important for understanding the air-water cycling of climatically This article was corrected on 25 JAN important trace gases (e.g., CO2,CH4,CH3Br, and N2O), and for aquatic metabolism studies using O2 mass 2019. See the end of the full text for fl details. balances. Gas uxes occur through three main pathways in wetlands. They could occur through (1) the aerenchyma of emergent vegetation (e.g., Dacey and Klug, 1979), (2) ebullition (e.g., Happell & Chanton, 1993), and (3) diffusive gas exchange across the air-water interface. The study here is focused on the latter, and on assessing processes that control the gas transfer velocity in emergent wetlands. In most aquatic environments, the air-water gas transfer velocity is controlled by near-surface turbulence. Whereas wind is the dominant mechanism for generating turbulence in lakes and in the ocean (Ho et al., 2011; Wanninkhof et al., 1987), sources of energy for near surface mixing in large wetlands may also include rain, flow around emergent vegetation, and wind-induced movement of emergent vegetation (e.g., Foster- Martinez & Variano, 2016; Ho et al., 1997; Poindexter & Variano, 2013). Because very few systematic laboratory and field experiments have been conducted specifically to exam- ine gas exchange in wetlands (e.g., Happell et al., 1995; Poindexter & Variano, 2013; Variano et al., 2009), wind speed/gas exchange parameterizations developed for lakes have been used to determine gas trans- fer velocity in these environments (e.g., Hagerthey et al., 2010). However, the relationship between wind speed and momentum flux has been found to be significantly different between open water environ- ments, such as lakes and the ocean, and wetlands with emergent vegetation (Tse et al., 2016). Because of the existence of vegetation (floating, emergent, and submerged), limited fetch, and shallow depths, the relationship between wind speed and gas exchange in wetlands could be significantly different than in open waters. Therefore, unlike lakes and the ocean, wind might not be the dominant factor driving gas exchange in wetlands. For example, waterside thermal convection has been found to be important in the absence of wind (MacIntyre et al., 2010; Poindexter & Variano, 2013). Rainfall increases turbulence on the fl ©2018. American Geophysical Union. water surface and also changes the heat ux because rain is often colder than the water surface on which All Rights Reserved. it falls (Ho et al., 1997, 2000).
HO ET AL. 178 Journal of Geophysical Research: Biogeosciences 10.1002/2017JG004299
Vegetation in wetlands can affect air-water gas exchange in multiple ways. Emergent vegetation can affect air-water gas exchange by (1) sheltering the water surface from wind and creating a shear-free region, (2) increasing turbulence as water flows around the plant stems and through wind-induced plant movement, and (3) influencing large-scale water movement. Floating vegetation (e.g., Nymphaea spp.) may act as a barrier for air-water gas exchange. Submerged vegetation (e.g., Utricularia spp.) in the Everglades ridge-slough habitat has been shown to be a significant factor controlling velocity in the upper part of the water column (Larsen et al., 2009; Leonard et al., 2006), which could affect air-water gas exchange. Linkages between emergent vegetation patterning, surface water flow vectors, and water depth fluctuations are well documented in emergent wetlands (Eppinga et al., 2008; Larsen et al., 2007; Rietkerk et al., 2004). For example, in undisturbed portions of the Everglades, the dominant emergent vegetation, sawgrass (Cladium jamaicense), forms elongated and slightly elevated ridges that are oriented in patterns parallel to the prevail- ing flow direction. The shallow (<1 m) surface water flows in this system are therefore concentrated between ridges in the deeper-water sloughs, which are characterized by an order of magnitude lower emergent plant stem densities (He et al., 2010; Leonard et al., 2006). Recent results from simulation models that couple surface water and vegetation dynamics suggest that the ridge-slough patterns in the Everglades, and the prevailing slough flow velocities and water depths, are the result of a complex set of feedback between the landscape-scale water mass balance, Cladium flooding tolerance, variable ridge-slough resistance to overland flow, and nutrient and sediment transport and redis- tribution (Cheng et al., 2011; Harvey et al., 2017; Kaplan et al., 2012; Larsen et al., 2007). These feedbacks, in turn, influence many of the factors (e.g., wind fetch and water flow velocities) that govern air-water gas exchange.
The goals of the study presented here are (1) to measure gas transfer velocity using sulfur hexafluoride (SF6) evasion experiments in the Everglades and (2) to determine how wind, rain, water flow, waterside convection, and vegetation contribute to air-water gas exchange in a shallow water environment populated by floating, emergent, and submerged vegetation. The results also provide a better understanding of how changes in wetland hydrology and vegetation patterns resulting from management practices or climate variability may impact dissolved gas dynamics.
2. Methods 2.1. Study Site The study was conducted in the Everglades of south Florida, USA, in an area known as “the pocket,” between the L-67A and L-67C levees and canals in water conservation area (WCA) 3A (Figure 1).
Specifically, SF6 tracer release experiments (TREs; see below) were conducted at sites designated RS1, RS2, and C1. The area is characterized by peat-based ridges dominated by emergent sawgrass (Cladium jamaicense) that are inundated during periods of seasonally high water, separated by deeper water sloughs (generally <1 m depth) containing floating and submerged vegetation. These wetlands are also characterized by the presence of large amounts of periphyton, which covers floating vegetation, such as Utricularia spp., as well as the organic substrate that is exposed between patches of thick emergent or floating vegetation. In 2013, a culvert (called S-152) was installed at the L-67A levee upstream of the study sites to experimentally increase flow across the pocket, in order to test hypotheses about landscape formation and ecosystem restoration as part of a project knows as the Decompartmentalization Physical Model (DPM; Larsen et al., 2017). The installation of this culvert created an opportunity to examine gas exchange under different flow conditions. Experiments conducted in 2009, 2011, and 2014 are reported here. The results from the 2009 experiment represent baseline conditions, such that the vegetation and water depth patterns at the study site were typi- cal of conditions prior to the culvert installation. A fire burned through the study site in June 2011, before the experiment reported here, during which emergent vegetation burned to the waterline. In 2014, the emergent vegetation had returned, and the S-152 culvert was opened, thereby increasing the flow in the wetland. The experimental conditions are summarized in Table 1. Sampling events are referred to below using a year and location nomenclature (e.g., 2011 C1).
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Figure 1. Map showing the locations of the SF6 tracer release experiments (RS1, RS2, and C1), the S-152 culvert installed as part of the DECOMP Physical Model (DPM), and the 3AS3WX weather station.
2.2. Limnocorrals During 2011 and 2014, limnocorrals made of PVC (polyvinyl chloride) were setup in the wetland at RS1 and
C1, respectively, to conduct control volume SF6 evasion experiments. The experiments allowed the effect of water flow, vegetation, and bottom roughness to be eliminated. Each limnocorral was fully enclosed on the side and bottom, with an inflatable ring that held up the sidewalls. The limnocorrals were filled with surface water from the wetland. Two limnocorrals, with diameter of 1.1 m, were deployed in 2011. They had mean water depths of 47 and 48 cm, respectively. The one deployed in 2014 had a diameter of 3 m and a mean
Table 1 Summary of Experimental Conditions in the Everglades in 2009, 2011, and 2014 21 Oct 2009 24 Oct 2011 28 Oct 2011 1 Nov 2011 14 Nov 2014 9 Nov 2014 Start 10:05 11:25 9:22 9:36 7:54 11:40
26 Oct 2009 27 Oct 2011 31 Oct 2011 4 Nov 2011 17 Nov 2014 12 Nov 2014 Date and time (local) End 15:54 17:30 16:24 16:04 13:52 16:22
Site RS2 RS1 C1 RS2 RS1 C1 Flow conditions Preflow Preflow Preflow Preflow Flow Flow Vegetation Normal Low Low Low Normal Normal Water temperature (°C) 23.4 ± 1.2a 23.8 ± 1.4 23.4 ± 2.6 24.2 ± 2.1 22.7 ± 1.4 22.2 ± 1.6b Water depth (cm) 55 ± 8 44 ± 7 51 ± 7 56 ± 6 55 ± 5 55 ± 5 EDEN Site 69E depth 55 ± 0.5 48 ± 0.2 51 ± 2.9 56 ± 0.1 53 ± 0.2 54 ± 0.5 Air temperature (°C) 24.9 ± 2.7 23.9 ± 2.7 24.2 ± 1.8 23.5 ± 1.9 22.0 ± 3.0 19.5 ± 2.8 Water-air temp difference (°C) 1.5 0.1 0.8 0.7 0.7 2.7 Relative humidity (%) 80.4 ± 12.9 72.1 ± 12.2 86.5 ± 7.6 73.5 ± 12.7 82.0 ± 12.9 77.2 ± 15.8 Wind speed at 10 m (m s 1) 5.1 ± 1.6 4.1 ± 1.6 4.7 ± 1.9 4.4 ± 2.0 3.2 ± 1.5 3.3 ± 1.1 Wind speed range (m s 1) 2.0–9.9 0.7–7.7 0.8–8.5 0.7–8.1 0.1–7.2 0.6–5.8 Rain amount (mm) 12.7 0.0 136.1 0.0 0.0 12.7 Max rain rate (mm h 1) 30.5 0 152 0 0 30.5 Average rain rate (mm h 1) 0.1 0 3 0 0 0.2 Barometric pressure (mbar) 1013.25 ± 1.91 1014.52 ± 2.11 1011.52 ± 2.19 1015.28 ± 2.44 1018.36 ± 1.98 1012.96 ± 1.40 Mean incoming solar radiation (W m 2) 389 384 210 391 333 382 Mean outgoing heat flux from water (W m 2) 91 91 49 93 107 113 ADV velocity (cm s 1) - Ridge n/a 0.35 0.42 0.25 3 n/a ADV velocity (cm s 1) - Slough 0.23c 0.4 0.37 0.20 3 0.74 aCalculated from temperature measured on the airboat during the day, the difference between average temperatures measured during the day, and the average temperatures measured at the fixed stations during all years. bFrom RS1; the data are in agreement with temperatures measured at the downstream end of the S-152 culvert. cFrom November 2010.
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water depth of 58 cm. The inflated ring protruded above the water in the surrounding wetland by ~15 and 20 cm in 2011 and 2014, respectively, and hence also limited the direct effects of wind on the water surface in the limnocorrals (Eggleston, 2011).
2.3. Determining Gas Transfer Velocity fl 1 The air-water ux of SF6 (FSF6 ) depends on the gas transfer velocity for SF6 (kSF6 ;cmh ) and the SF6 concen- tration gradient between the water ([SF6]w) and the air ([SF6]a), modified by the Ostwald solubility coefficient of SF6 (α) (Bullister et al., 2002): ÀÁ ¼ ½ α½ : FSF6 kSF6 SF6 w SF6 a (1)
For the experiments here, kSF6 was determined using SF6 evasion experiments, by injecting SF6 into the limnocorrals or wetland surface water and then monitoring the change in SF6 concentration in water over time (see below). Because of the low concentration of SF6 in the atmosphere (~6.8 to 8.4 pptv in the Northern Hemisphere from 2009 to 2014 (National Oceanic and Atmospheric Administration, 2017)), and
its low α (~0.005 at 20°C in freshwater), α[SF6]a in these experiments was negligible compared to [SF6]w α and can be ignored in equation (1). Neglecting [SF6]a, experimentally, FSF6 is related to the change in [SF6]w as follows, where a positive flux is gas evasion (Wanninkhof et al., 1987):
d½ SF F ¼ h 6 w ; (2) SF6 dt
where h (in cm) is the mean depth of the water. Combining these equations (1) and (2) and integrating over
time to solve for kSF6 : t 1 d½ SF k ¼ h ∫ 6 w ; (3) SF6 ½ 0 SF6 w dt yields the following expression: Δln½ SF k ¼ h 6 w : (4) SF6 Δt
Δln½ SF 6 w fi For each experiment presented here, Δt was determined with linear least squares t to ln[SF6]w versus t.
In the wetland experiments, the average SF6 concentration for each day, determined from the volume of
water sampled and the mass of SF6 in that volume, was used with equation (4) to determine kSF6 . In the lim-
nocorrals, each SF6 measurement was used directly with equation (4) to calculate kSF6 .
In order to compare the results with other gases and in different conditions, kSF6 was normalized to a Schmidt number (Sc; kinematic viscosity of water divided by diffusivity of that gas in water) of 600, k(600), correspond-
ing to k for CO2 at 20°C: 2=3 ðÞ¼ 600 ; k 600 kSF6 (5) ScSF6 where the Sc exponent of 2/3 corresponds to that for a nonwavy water surface (Jähne et al., 1987). The Sc for fi SF6, ScSF6 , was calculated using the coef cients compiled by Wanninkhof (2014) for freshwater, and the ScSF6 during the experiments are given in Table 2.
2.4. SF6 Injections For the wetland injections, a 20 L high-density polyethylene container was filled with water from the wetland,
and then infused with SF6 by bubbling from a compressed gas cylinder of 99.99% SF6. The saturated solution was injected as a point source at each study site by carefully pouring the water into the wetland to avoid 3 creating bubbles. The total amount of SF6 injected each time was ~4.6 × 10 mol. For the limnocorral injections, a 50 mL crimp top borosilicate glass serum bottle with a butyl rubber septum
was filled with ~30 mL of water, and the remaining volume (i.e., the headspace) was filled with 99.99% SF6.
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Table 2 Summary of Ridge and Slough Vegetation Characteristics at the Time of SF6 Tracer Experiments 2009 RS2 2011 RS1 2011 C1 2011 RS2 2014 RS1 2014 C1
Ridge Sampling dates 28 Sep 2010 1 Nov 2011 1 Nov 2011 2 Nov 2011 15 Aug 2014 15 Aug 2013 Canopy height above water (cm) 27 34 38 15 43 25 Stem biovolume above water (10 4 cm3 cm 3) 38.6 1.3 0.8 0.2 8.1 8.4 Stem biovolume below water (10 4 cm3 cm 3) 57.6 5.4 7.1 7.6 64.7 20.8 Slough Sampling dates 28 Sep 2010 1 Nov 2011 1 Nov 2011 2 Nov 2011 15 Aug 2014 6 Nov 2012 Canopy height above water (cm) 14 24 34 16 1.3 25 Stem biovolume above water (10 4 cm3 cm 3) 0.4 0.5 0.8 0 0.3 1.3 Stem biovolume below water (10 4 cm3 cm 3) 4.4 3.6 2.1 1.3 0.7 2.3
Note. The measurement uncertainties are ±5% for canopy height above water and ±10–15% for stem biovolume; grey shading indicates the year of a major fire that burned through the experimental area in mid-June prior to the experimental measurements in the fall.
After allowing the water to equilibrate with the headspace, a predetermined amount of water (enough to 11 1 achieve an initial SF6 concentration of ~1.3 × 10 mol L in the pool) was removed from the bottle with a 1 mL syringe via a needle, and injected into the pool.
2.5. SF6 Measurements 2.5.1. Wetland
After allowing the SF6 to mix overnight in the wetland, the distribution of SF6 was sampled and measured from an airboat using an automated SF6 analysis system (Ho et al., 2002, 2009) in a stop-and-go mode described in Variano et al. (2009), over the course of 4 to 6 days. Measurements were made perpendicular to the flow path,
and the sampling was conducted on an adaptive grid, based on the SF6 concentration in the water.
Briefly, the SF6 system consisted of an extraction, gas separation, and analytical systems. At each stop, water from the wetland was pumped through a tangential flow filter that allowed large particles to be bypassed,
then through a series of fine mesh filters (80 and 15 μm) into a membrane contactor, where SF6 and other gases were extracted out of the water and sent to the gas separation system (i.e., the gas chromatograph
(GC)) by ultrahigh purity (UHP; 99.999%) N2. In the gas separation system, SF6 was separated from other gases with a 2 m molecular sieve 5A (80/100 mesh) column kept at ambient temperature. Then the sample was directed to the analytical system, an electron capture detector (ECD) for quantification. Together, the gas separation and analytical system are referred to as the GC/ECD. Analytical precision based on repeated mea-
surements of the 203.5 pptv SF6 standard on a 0.335 mL loop was ±2%. 2.5.2. Limnocorrals In the limnocorrals, after injection, the water was mixed gently by hand over an hour. Then, over the course of 3 and 5 days during the 2011 and 2014 campaigns, respectively, two to four samples of water (20 to 30 mL)
for discrete SF6 measurements were taken in 50 mL glass syringes with polycarbonate stopcocks every 30 to 60 min during the day. The syringes were stored underwater in a cooler until they were transported to the
laboratory at the end of the day. SF6 was measured using a headspace method described in detail by Wanninkhof et al. (1987).
Briefly, in the laboratory, a headspace was created in the syringe with UHP N2 and shaken for at least 3 min to equilibrate the SF6 in the water with the headspace. Then, the headspace was pushed through a Mg(ClO4)2 drying tube into a sample loop, which was then injected into the GC/ECD. The SF6 was separated from other gases with a 2 m molecular sieve 5A (80/100 mesh) column kept at ambient temperature. The analytical precision of this setup, based on analysis of a standard during the experiment, was ±0.9%. 2.6. Meteorological Measurements During the experiments, wind speed, rain rate, total incoming solar radiation, net radiation, relative humidity, and air temperature were measured at a nearby meteorological station (3AS3WX; Figure 1) deployed in the wetland by the South Florida Water Management District (DBHYDRO Browser, 2017). Instantaneous
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measurements were measured every 15 min, and the frequency for rain rate measurements was increased to once per minute when rain was detected. Rain rate was measured with a tipping bucket rain gauge (Hydrological Services TB3), total incoming solar radiation was recorded using a pyranometer (LI-COR LI-200R), net radiation was measured with a net radio- meter (Kipp & Zonen NR Lite2), and relative humidity and air temperature were measured with a humidity and temperature probe (Vaisala HMP155). Wind speed was measured using a propeller anemometer (RM Young Wind Monitor 05103) mounted on a 10 m tower. During the 2011 experiments, an additional tower was installed at RS1, with two 2-D sonic anem- ometers (Vaisala WMT700) at 0.08 and 2.6 m and a propeller anemometer (RM Young Wind Monitor 05103) at 5.3 m above the water surface.
Wind speed can be related to the friction velocity (u*a) as follows, assuming a log profile for wind speed: u a z uz ¼ ln (6) κ z0
where uz is the wind speed at height z, κ is the von Kármán constant (0.4), and z0 is the roughness length. The z0 indicates the height where uz no longer follows a log profile, due to, for example, roughness element such as emergent vegetation in a wetland; it is typically 1/10 of the height of the roughness element. The wind
speed at a reference height of 10 m, u10, could be calculated from equation (6) if u*a and z0 are known. With the wind speed measurements at two different heights, two realizations of equation (6) could be solved
simultaneously to derive u*a and z0: κðÞ u2u1 u a ¼ (7) ln z2 z1 uzκ z0 ¼ exp lnðÞ z (8) u a
where u1 and u2 are wind speed measurements at heights z1 and z2, respectively.
2.7. Water Depth and Temperature In the wetland, each time the airboat made a sampling stop, four water depth measurements were made around the boat using a stainless-steel wading rod. The depth measurements were similar to depths measured by a nearby gauging station (EDEN Site 69E; see Table 1), where the water level was referenced to the North American Vertical Datum of 1988 (NAVD88). Water depths in the limnocorrals were measured at multiple locations each day with a stainless-steel wading rod. Depths in the limnocorrals varied slightly due to small variations in the underlying substrate. Water temperature in the wetland was recorded during the day from the airboat. In addition, time series mea- surements were made, at a temporal resolution of 10 to 15 min, using nickel resistance temperature detectors (RTD; KPSI; ±0.1°C accuracy) deployed at the study sites. In 2009, no RTD measurements were available, so the average difference (2.4°C) obtained in 2011 and 2014 between measurements made on the airboat during the day and the RTD measurements was subtracted from the 2009 airboat measurements. Water tempera- ture in the limnocorrals was recorded with thermistors (RBR; ±0.002°C accuracy) at a temporal resolution of 5 s, averaged and recorded every 30 s. 2.7.1. Small- and Large-Scale Water Velocities Through the Wetland Small-scale water flow velocity was measured at approximately the midpoint of the water column at sites C1, RS1, and RS2 using 10 MHz up/down/side-looking acoustic Doppler velocimeters (ADV; SonTek/YSI and Nortek) at a frequency of 10 Hz following the procedures of Harvey et al. (2009). The data were recorded in 1 min bursts (600 samples) and collected every 15 min. Velocity profiles were also measured vertically at 2–5 cm depth increments in the water column at 10 Hz in 1 min bursts by adjusting the height of the ADV, yielding 600 samples at each depth. Velocity profile data underwent the same corrections and filters as the continuous velocity data. The ADVs can measure flow velocity to a resolution of 0.01 cm s 1 (SonTek/YSI) and 0.1 cm s 1 (Nortek) with an accuracy of 1% and 0.5% of measured velocity, respectively. The measurement volume is approximately 1 cm3 and represents small-scale measurements that might be heterogeneous in time and space.
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Large-scale advection and lateral and longitudinal dispersion (Ky and Kx, respectively) were determined from the evolution of the daily SF6 distribution according to methods described in Ho et al. (2009) and Variano et al. (2009). Using these methods, the movement of the center of mass of the SF6 patch was used to deter- mine net advection, and the time evolution of the two-dimensional distribution of the SF6 patch was used to determine Ky and Kx. 2.7.2. Vegetation Characteristics Vegetation stem densities were determined by harvesting of vegetation in 0.25 m2 clip plots and measuring the distribution of stem diameters and frontal areas following the procedures of Harvey et al. (2009).
Vegetation sampling occurred near the time of the SF6 TREs, with adjustments made in reporting variables such as vegetation canopy height above water to account for differences in water depth between the time
of vegetation sampling and the time of the SF6 TREs. Measurements in 2011 reflect the effects of a major fire that burned through the experimental area in mid-June prior to the tracer and vegetation measurements, which were made in late October–November. Measurements were not made at C1 in 2014, so those made around the same time period in 2012 and 2013 are shown in Table 2. Within a desired sampling area, the vegetation was sampled by positioning quadrats using a stratified
random sampling scheme at ridge and slough locations at all the sites where the SF6 TREs were conducted. Once the quadrats were situated, total canopy height and water depth were recorded, and all the vegetation above the water surface was clipped and bagged as one sampling increment. Below the water surface, vege- tation was sampled in 15 or 20 cm increments proceeding from the water surface to the sediment water interface. Sample increments intersecting the bed were clipped at the floc surface. Vegetation samples were bagged, and stored in the dark and on ice for transport to the laboratory for further processing. In the laboratory, sample increments were spread out and categorized by species. Measurements of stem diameter and length were collected for the purpose of calculating the average diameter and the frontal area of stems, i.e., the exposed area of stem per unit volume in the water column. First the number of stems and leaves were counted for Cephalanthus occidentalis, Cladium jamaicense, Justicia angusta, Nymphaea odorata, and Panicum hemitomon. The width of 10 randomly selected stems were measured for each species, with width being measured as the distance across the middle of each stem fragment along the widest dimension (major axis) and across the narrowest dimension (minor axis) as measured using a micrometer. For every leaf (or if there were greater than 10 leaves, 10 were randomly chosen) the width, length, and thickness were measured using a ruler or micrometer. Frontal area and dimensional volume were then cal- culated as d þ d A ¼ 1 2 n; (9) f 2
1 where Af is projected frontal area per unit volume (cm ), d1 is average stem diameter of axis 1 (major axis; 2 cm), d2 is average stem diameter of axis 2 (minor axis; cm), and n is the number of stems per unit area (cm ). Stem biovolume per unit bulk volume was calculated for all species except sawgrass as follows: 1 V ¼ πd d n; (10) 1 2 4 with a different equation used for sawgrass, due to its “v” shape cross section: 1 V ¼ d d n: (11) sawgrass 1 2 2
3. Results and Discussion 3.1. Meteorology
Wind speeds, u10, were variable throughout each of the six experiments, but the mean u10 was similar for each experiment, ranging from 3.2 ± 1.5 to 5.1 ± 1.6 m s 1 (mean ± SD). The experiment in 2009 had the high- 1 1 est u10 of all the experiments, where u10 was as high as 9.9 m s and never dropped below 2 m s . The 1 experiments in 2014 had the lowest u10, averaging around 3 m s and with maximum u10 of 5.8 and 7.2 m s 1 (Table 1). The prevailing wind direction was from the NE for most of the experiments, except for 2009 RS2 when there were winds from NNW and 2014 C1 when it was from NW.
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Wind speed measurements made at multiple heights from RS1 in 2011 were used in conjunction with equa-
tions (7) and (8) to derive z0, which, in the absence of the usual emergent wetland vegetation because of the fire, was determined to be 0.023 m. In November 2010, two 3-D sonic anemometers (Gill Windmaster Pro) were installed in the wetland at 0.85 and 3 m above the mean water level at site RS2 (Eggleston, 2011).
Analysis of these data indicates that when emergent vegetation was present, z0 was 0.189 m, almost an order of magnitude greater than without vegetation. Due to similar vegetation characteristics (see below), the
experiments conducted in 2009 and 2014 are assumed to have similar z0. Rain was present during half of the experiments (Table 1), and while it was relatively light during the 2009 and 2014 experiments (total rain amount: 12.7 mm, each, with maximum rain rate up to 30.5 mm h 1), it was hea- vier during the 2011 experiment (total rain amount: 136.1 mm, with maximum rain rate up to 152 mm h 1). Total incoming solar radiation varied with cloud cover but was similar between experiments except during 2011 C1, where it was ~50% lower due to extensive cloud cover. Net outgoing radiation was mainly controlled by the water temperature, which determines the upwelling longwave radiation, and air tempera- ture, water vapor content, and clouds, which determines the downwelling longwave from the atmosphere. The values are significantly lower during 2011 C1, and slightly higher during 2014 experiments, when the water temperature was appreciably greater than air temperature (Table 1).
3.2. Water Depth and Temperature For the different experiments, water depth measurements made from the airboat varied between 44 ± 7 and 55 ± 8 cm (Table 1). To compare these airboat measurements to water depth measurements made at a fixed site (EDEN Site 69E, reference to NAVD88), the 2009 value from EDEN Site 69E was adjusted to the airboat measurement ( 169.7 cm), and the same offset was applied to the other years. The agreement between the measurements is good (within 0–2 cm), except in 2011 RS1 (4 cm), but those measurements are still within the uncertainty (Table 1). There was a diurnal pattern to the water temperature, but the maximum and minimum temperature during a
24 h period usually varied by less than 1°C. The mean of the measurements during each SF6 TRE was between 23.0 ± 1.6 and 26.9 ± 2.6 °C (Table 1).
3.3. Vegetation Emergent vegetation was denser on ridges compared with sloughs, with an order of magnitude greater stem biovolume both above and below water, and a canopy that stood typically more than twice as high above the water surface in ridges compared with sloughs (Table 2). The canopy height above the water ranged between 15 and 43 cm on ridges and between 16 cm below the water surface to 14 cm above in sloughs. When comparing vegetation between different years and different sites, it is most instructive to examine the stem biovolume of the ridges both above and below water, because the sloughs are usually relatively free of vegetation compared to the ridges (Table 2). These spatial and temporal variations in vegetation biovolume affect drag and turbulence and could produce secondary vertical flows in the water column (Nepf, 1999; Nepf & Koch, 1999), all of which could influence air-water gas exchange. Variation in canopy height alters wind effects, with denser and taller canopies above the water dissipating the effects of wind on the water surface as shown above. The fire in June 2011 decreased the stem biovolume on ridges by tenfold or more compared with sloughs, both above and below the water surface. Slough biovolumes did not appear to be affected by the fire. The decrease of biovolume on the ridges would make them more like sloughs with respect to their influence on wind and water flow, allowing the wind to have a more direct affect in moving water in the wetland, but might cause the water flow to generate less turbulence from flow around emergent vegetation.
3.4. Water Velocity, Advection, and Dispersion Point measurements of water flow velocities made in 2010 (used here as a proxy for 2009 because no mea- surements were available) and 2011 showed similar values, between 0.2 and 0.42 cm s 1 (Table 1). With the opening of the S-152 culvert, the flow velocities increased to 3 cm s 1 for 2014 RS1 and 0.74 cm s 1 for 2014 C1.
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Table 3 Summary of Results From SF6 Tracer Release Experiments in the Everglades in 2009, 2011, and 2014 Date 21–26 Oct 2009 24–27 Oct 2011 28–31 Oct 2011 1–4 Nov 2011 14–17 Nov 2014 9–12 Nov 2014
Site RS2 RS1 C1 RS2 RS1 C1 Sc(SF ) 805 790 805 775 834 854 6 k(600) (cm h 1) 1.1 ± 0.3 2.3 ± 0.5 3.2 ± 0.2 2.5 ± 0.4 2.2 ± 0.2 2.7 ± 0.7 SF Heading (°) 141 ± 6.2 148 ± 2.5 109 ± 3.1 106 ± 4 171° → 155° 67° → 87° → 100° → 120° 6 Advection (cm s 1) 0.05 ± 0.01 0.11 ± 0.01 0.15 ± 0.08 0.13 ± 0.03 0.43 ± 0.04 0.32 ± 0.02 Longitudinal dispersion (cm2 s 1) 323 ± 122 998 ± 227 1068 ± 226 819 ± 123 173 ± 119 1278 ± 338 Lateral dispersion (cm2 s 1) 1.2 ± 1.5 13.2 ± 8.6 72.3 ± 33.9 98.1 ± 20.1 4.5 ± 2.5 2.1 ± 0.5
Note. Errors for k(600), SF6 heading, advection, longitudinal dispersion, and lateral dispersion are the standard error of the least squares fit to the data used to derive those variables.
1 From changes in the SF6 distribution, net advection rate at RS2 was calculated to be 0.05 cm s during 2009, and increased by a factor of 2.5 to 0.13 cm s 1 at the same site in 2011 (Table 3). The net advection rates at the other sites in 2011 were of similar magnitude. Changes were more dramatic from 2011 to 2014 with the opening of the S-152 culvert, when net advection rate increased by factors of 4 and 2 at RS1 and C1, respectively.
Ky and Kx also increased dramatically from 2009 to 2011 (Table 3 and Figure 2), probably due to the fact that wind had a more direct effect on water flow when there was less emergent vegetation. In 2014, Ky returned to near 2009 values. However, while the Kx was low at 2014 RS1, Kx at 2014 C1 was similar to values at 2011 C1. This difference probably reflects the fact that the water took a relatively straight path at RS1, whereas the landscape hydraulic gradient at C1 is such that there was significant curvature to the flow path (Figure 2),
thereby increased the velocity differences in the SF6 patch.
The net advection rates measured with SF6 are lower than the point measurements of velocities made with ADVs because the ADVs aimed to measure the maximum velocities in the water column, whereas advection
was determined from the movement of the center of mass of SF6, which has contribution from a distribution of velocities.
3.5. Gas Transfer Velocities 1 For the six SF6 experiments in the wetland, k(600) ranged from 1.1 to 2.8 cm h (Table 3). In 2009, during the baseline study, k(600) was 1.1 ± 0.3 cm h 1, and increased by a factor of ~2 to 3 in 2011 and 2014. For the limnocorral experiments (Table 4), because water was sheltered from the wind by the elevated rim and there was no water flow or emergent vegetation in the limnocorral, gas exchange was driven mainly by waterside thermal convection. In 2011, k(600) in the two limnocorrals were 0.52 ± 0.03 and 0.52 ± 0.02 cm h 1 over 3 days, and in 2014, k(600) was 0.61 ± 0.02 cm h 1 over 5 days (Table 4). In other words, for the baseline condition, waterside thermal convection was responsible for nearly half of the k(600) measured.
3.6. Comparison With Previous Measurements The baseline k(600) results from 2009 presented here are in line with the few previous measurements in emergent wetlands, but the results from 2011 and 2014 are generally higher. Variano et al. (2009) conducted
SF6 experiments in several locations of the Everglades (WCA-3A and 3B), and the results were fitted with an optimization model to yield k(600) that ranged between 0.3 and 1.4 cm h 1, assuming a Sc 2/3 dependence. fl Happell et al. (1995) used a oating dome in another part of the Everglades to measure kCH4 and derived 1 2/3 results that are equivalent to a mean k(600) of 0.77 ± 0.55 cm h (n = 25; ScCH4 = 617; Sc ).
3.7. Factors Influencing Gas Transfer Velocities To separate the influence of rain and waterside thermal convection on k(600) from that of wind and water flow around emergent vegetation, the effects were examined separately and assumed to be additive. This is the simplest assumption that could be made a priori, without detailed experiments to examine how the
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Figure 2. Composite SF6 distribution at each study site during each experiment. The color of the symbols indicates SF6 concentration, where warmer colors (i.e., red) are higher concentrations.
effects of each of the processes might interact. The effects of rain and waterside thermal convection were determined using established parameterizations. To determine the effect of rain on gas exchange during the experiments, a parameterization between rain
rate and k(600)rain was obtained based on refitting the laboratory data of Ho et al. (1997, 2000) to yield ðÞ¼ : 0:704; k 600 rain 2 066R (12) where R is rain rate (in mm h 1) of natural rain with a raindrop size distribution described by Marshall and Palmer (1948). In the three experiments where rain was present, k(600) due to rain for the individual experi- ments ranged from 0.13 to 1.29 cm h 1 (Table 5).
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Table 4 For gas transfer due to waterside thermal convection, Poindexter and Summary of Experimental Conditions and Results From Limnocorral Experiments Variano (2013) proposed from scaling arguments that k(600)convection 2–4 2–4 13–17 could be parameterized by the heat flux from the water to the Date Nov 2011 Nov 2011 Nov 2014 atmosphere: Site RS1 RS1 C1 1=4 = qgβa2 600 2 3 Water temperature (°C) 24.2 ± 0.7 24.4 ± 0.7 22.6 ± 0.3 ðÞ ¼ 3=4 ; k 600 convection A ν ρ (13) Water depth (cm) 47.3 ± 1.1 48.3 ± 1.3 57.8 ± 2.6 cp Pr Air temperature (°C) 23.5 ± 1.9 23.5 ± 1.9 22.0 ± 3.0 where q is the net heat flux, g is acceleration due to gravity, Pr is the Relative humidity (%) 73.5 ± 12.7 73.5 ± 12.7 82.0 ± 12.9 Rain Amount (mm) 0 0 0 Prandtl number (i.e., kinematic viscosity of water divided by thermal Barometric 1014.29 ± 2.71 1014.29 ± 2.71 1017.37 ± 2.27 diffusivity in water) at the temperature of the water during the
Pressure (mbar) measurement, and a, β, ν, cp, and ρ are the thermal diffusivity, thermal Mean incoming solar 374.4 374.4 390.5 expansion coefficient, kinematic viscosity, isobaric specific heat radiation (W m 2) capacity, and density of water, respectively, and A is an empirical Mean outgoing 98.2 98.2 116.3 fi heat flux from coef cient that relates the Nusselt number to the Rayleigh number. water (W m 2) Equation (13) is valid for situations where heat flux is out of the water Sc(SF6) 775 767 838 (i.e., q < 0) and where heat transfer is primarily via convection (i.e., 1 k(600) (cm h ) 0.52 ± 0.03 0.52 ± 0.02 0.61 ± 0.02 Rayleigh number > 8×106); the latter condition is usually met in wet- Note. The errors represent the standard deviation from the mean, except for lands deeper than ~10 cm (Poindexter & Variano, 2013). Poindexter k(600), which was derived from uncertainties in the SF6 measurements versus and Variano (2013) chose A = 0.14 from Martynenko and Khramtsov time. (2005). Equation (13) is similar to that used by Soloviev et al. (2007), but with a different A (0.25) determined by Ginzburg and Federov (1978) in laboratory experiments. Katsaros et al. (1977) proposed A = 0.156 in laboratory experiments with freshwater. The limnocorral data from the Everglades are consistent with A = 0.10 (Table 5). The radiative flux imbalance during each experiment, determined as the difference between the net total radiation measured by the net radiometer and incoming shortwave radiation measured by the pyranometer, is attributed to the sum of sensible and latent heat fluxes into or out of the water (i.e., the net heat flux, q), ignoring horizontal heat transport in the water. For the different experiments, the averaged 2 heat flux out of the water varied between 49 and 113 W m (Table 1), and k(600)convection during the experiments ranged from 0.45 to 0.58 cm h 1 (Table 5). Equation (13) could be approximated by the follow- ing expression, when the water temperature, T (in °C), is between 6 and 40°C: 2=3 = ÀÁ600 kðÞ600 ¼ ðÞq 1 4 1:5033 þ 2:0913 T 0:29793 for q < 0; (14) convection Pr where Pr is the Prandtl number at T, and by convention q is negative for outgoing flux (i.e., q would be a positive quantity).
Table 5 Estimates of Gas Transfer Velocities, k(600) (cm h 1), Made Using Existing Gas Exchange Parameterizations According to the Experimental Conditions in 2009, 2011, and 2014, and Those Quantified With SF6 Tracer Release Experiments in This Study 21–26 24–27 28–31 1–4 14–17 9–12 Date Setting/process Oct 2009 Oct 2011 Oct 2011 Nov 2011 Nov 2014 Nov 2014
Site RS2 RS1 C1 RS2 RS1 C1 Cole and Caraco (1998) Wind/lake 5.7 4.6 5.3 5.1 3.8 3.8 MacIntyre et al. (1995) Wind/lake 6.8 4.9 6.2 5.7 3.3 3.3 Ho et al. (2006) Wind/ocean 7.5 5.1 6.8 6.2 3.2 3.2 O’Connor and Dobbins (1958) Estuary/currents and water depth 0.46 0.77 0.83 0.74 1.36 1.17 Ho et al. (1997) Rain 0.13 0 1.29 0 0 0.22 Poindexter and Variano (2013) Wetlands/convection 0.55 0.56 0.45 0.57 0.58 0.56 (using coefficient A = 0.1) k(600)measured 1.1 ± 0.3 2.3 ± 0.5 3.2 ± 0.2 2.5 ± 0.4 2.2 ± 0.2 2.7 ± 0.7 k(600)measured k(600)rain 1.0 2.3 1.9 2.5 2.2 2.5 k(600)measured k(600)rain 0.4 1.7 1.5 1.9 1.6 1.9 k(600)convection k(600) calculated from equation (16) 1.1 2.2 3.4 2.2 2.3 2.5 Note. Also shown is the evaluation of equation (16) using rain, heat flux, and flow data obtained during the experiments.
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3.5 Rain When k(600) and k(600) are subtracted from the measured Flow rain convection Convection k(600), the residual is presumably due to wind and the effect of water flow 3.0 0.22 (8%) through the wetland. The residual includes uncertainties from, and 1.29 fl 2.5 (40%) turbulence generated by, submerged, emergent, and oating vegetation,
) and increased flow due to opening of culverts. It also includes the interac- -1 2.0 tion between vegetation, depth, and flow. The residual k(600) was 0.4 cm h 1 in 2009 and ranged from 1.5 to 1.9 cm h 1 in 2011 and 2014 1.9 1.9 1.5 1.7 (77%) 0.13 1.6 (71%) (Table 5). (12%) (75%)
(600) (cm h 1.5 (73%) k (46%) Because of the limited fetch and sheltering effects of the emergent 1.0 0.4 vegetation, the effect of wind on gas exchange in the Everglades is likely (37%) 0.5 predominately through contributing to water movement through the 0.55 0.56 0.45 0.57 0.58 0.56 wetland. The main driver for water velocity is the hydraulic gradient, but (51%) (25%) (14%) (23%) (27%) (21%) 0.0 the wind contribution could manifest as increases in advection and disper- 2009 RS2 2011 RS1 2011 C1 2011 RS2 2014 RS1 2014 C1 sion. Wind has also been show to increase gas exchange through Figure 3. Proportion of k(600) attributed to rain, water flow, and water side movement of emergent vegetation (Foster-Martinez & Variano, 2016), convection for each of the SF6 tracer release experiments. The numbers but this effect was not considered here. on the bars are k(600) attributed to each process, and the percentage relative fl to the total k(600). The gas transfer velocity due to ow, k(600)flow, found in these experi- ments (n = 6) could be modeled by
ðÞ¼ : ðÞ : : ðÞ: ðÞ : ðÞ : υ ; k 600 flow 1 718 ±0 0022 9 357 ±0 248 exp 39 504 ±0 546 (15)
1 for υ > 0.043, where υ (in cm s ) is the advective velocity derived from the SF6 tracer release experiments. The errors in equation (15) represent one standard deviation of the fit to the data. With the exception of the baseline experiment, 2009 RS2, flow was the predominate driver of gas exchange in the Everglades (Figure 3). Rain could be a major factor when it is present (e.g., 2011 C1), and there is always a substantial fraction of gas exchange due to heat flux and water side convection. The total gas exchange in the Everglades could be parameterized by this atrocious looking, but practical, expression:
kðÞ600 ¼ 2:066R0:704 þ ðÞ1:718 9:357 expðÞ 39:504υ (16) total 2=3 = ÀÁ600 þ ðÞq 1 4 1:5033 þ 2:0913 T 0:29793 for q < 0; Pr
where R is the rain rate (in mm h 1), υ is the advective flow rate (in cm s 1), q is the net heat flux (in W m 2), and T is the water temperature (in °C). Equation (16) was evaluated against the k(600) measured during the
SF6 TREs (k(600)measured), and within the error of the measured k(600), the results of equation (16) are in agreement with the data (Table 5). Because of the nonlinearity of the equation, with the exception of υ, it should be applied to the highest tem- poral resolution data possible, rather than the mean values. Furthermore, when q > 0, the net heat flux is into the water and the third term in equation (16) (i.e., the water side convection term) should be set to 0. Also, equation (16) is only for 6°C < T < 40°C. Specifically, for marshes such as those at high elevations or high lati- tudes where water is near 4°C, net heat flux into the water (i.e., q > 0) would cause convection and heat flux out of the water (i.e., q < 0) would stabilize the water column. In cases where q is not measured, it could be determined by the change in water temperature with time as follow: ΔT q ¼ ρC h; (17) Δt p
ΔT 1 ρ 3 where Δt is the change in water temperature with time (in °C s ), is the density of water (in kg m ), Cp is the heat capacity of water (in J kg 1 °C 1), and h is the water depth (in m). This expression could be approxi- mated by
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ΔT ÀÁ q ¼ 4215640 2430T þ 33:63T 2 0:413T 3 h; (18) Δt
where T is the water temperature (in °C).
3.8. Implications for Biogeochemical Studies in Wetland Ecosystems
To determine the flux of gas x (Fx) in wetlands, a combination of equation (1) and equation (5) can be used: = ÀÁSc 2 3 F ¼ kðÞ600 ½ x α ½ x x ; (19) x w x a 600
where [x]w and [x]a are the concentrations of x in the water and air, respectively; αx is the Ostwald solubility coefficient for x; and Scx is the Schmidt number for x. Because there is no gas exchange relationship developed specifically for emergent wetlands, some previous studies in wetlands requiring knowledge of gas transfer velocity have used wind speed/gas exchange parameterizations derived for lakes. For example, a study of ecosystem metabolism in the
Everglades based on a mass balance of dissolved O2 (Hagerthey et al., 2010) used a parameterization ðÞ¼: þ : 1:7 by Cole and Caraco (1998) developed for lakes (i.e., k 600 2 07 0 215 u10 ) to estimate air-water O2 exchange. Given the environmental conditions during the experiments shown here, using the Cole and Caraco (1998) parameterization would lead to k(600) that are 1.4 to 5.2 times higher than the measured k(600) (Table 5). Using another relationship developed for lakes, for example, one from MacIntyre et al. ðÞ¼: 1:64 (1995) (i.e., k 600 0 45 u10 ) would lead to k(600) that are 1.2 to 6.2 times higher than what was mea- sured (Table 5). Using wind speed/gas exchange parameterizations developed for estuaries or the ocean (e.g., Ho et al., 2006; O’Connor & Dobbins, 1958) would sometimes lead to even larger errors (Table 5). Any error in k(600) will translate directly to an error in the calculated gas flux. In aquatic ecosystems like emergent wetlands, the difference between gross primary production (GPP) and ecosystem respiration (R) represents the net ecosystem production (NEP). GPP increases the concen-
tration of O2 in the water, whereas R decreases it. Hence, for ecosystem metabolism studies, O2 mass fl balance has been used to determine NEP, with a correction for air-water ux of O2, FO2 (e.g., Hagerthey Δ ¼ Δ et al., 2010): O2 NEP FO2 , where O2 is the measured change of O2 in water column. For these ecosystem metabolism studies, if k(600) were over predicted, it would lead to an overprediction of
FO2.IfFO2 were negative (i.e., into the water), this would lead to an underestimate of NEP and hence GPP, and
overestimate of R. The opposite would be true ifFO2 were positive. For studies looking at diffusive CH4,N2O, or CH3Br fluxes from wetlands, overestimating k(600) would lead to overestimates of the fluxes of these greenhouse and ozone-depleting gases.
3.9. Implications for Ecosystem Restoration of the Everglades The experiments conducted here are part of a large-scale flow enhancement experiment called the DPM, which aims to study how decompartmentalization (i.e., removing barriers to flow such as levees and canals) might increase conveyance of water and transport of nutrients and sediments that could improve ecological conditions by preserving or restoring the characteristic ridge and slough landscape that provides prime habi- tat for fish and wildlife (Harvey et al., 2017). At approximately 3 × 3 km in size, the DPM prototypes the broader plan for Everglades restoration to increase water levels in the degraded wetlands, and increase con- nectivity and water flow from Lake Okeechobee to Everglades National Park (Davis et al., 2014). In the Everglades, persistent increases in phosphorus concentrations above natural background levels (<10 μgL 1) are thought to be responsible for significant changes in this ecosystem, including the wide- spread proliferation of cattails (Typha spp.) over sawgrass, shifts in algal and macroinvertebrate species, and overall decreases in habitat quality (Gaiser, 2009; Lodge, 2016; McCormick et al., 2004; Noe et al., 2001;
Sah et al., 2014). It has been shown that a negative correlation exists between dissolved O2 and phosphorus concentrations in wetlands (Day & Kemp, 1985), likely due to dissolved O2 levels changing the sediment redox conditions, leading to the exchange of phosphorous across the sediment-water interface (Mortimer, 1941, 1942).
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Therefore, air-water gas exchange, which resupplies dissolved O2 to the marsh water, could play a role in phosphorus cycles through the Everglades ecosystem. Since the results of the SF6 TREs show that increase in water flow will increase k(600), this provides another way that decompartmentalization could contribute to ecosystem restoration goals, and one that should factor into management decisions.
4. Conclusions
The SF6 tracer release experiments here show that because of the shallow water depths, limited fetch, and presence of floating, submerged, and emergent vegetation, gas transfer velocities in wetlands are influenced by many factors in addition to wind speed. Wind speed/gas exchange parameterizations developed for lakes or the ocean are not appropriate for wetlands and would typically predict gas transfer velocities that are too high. Air-water gas exchange in the Everglades is mainly affected by waterside convection and water flow, but rain can also play a significant role. On first order, gas exchange can be parameterized by rain rate, water flow velocity, and heat flux out of the water.
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Erratum Equation 14, which is repeated in Equation 16, has been corrected. It is now scaled by a factor of (3600*100). Equation 14 was originally published in units of m/s, but the results of Equation 16 was in cm/h. The two equations have been corrected, and this version may be considered the authoritative version of record.
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