Scaling relationships for diffusive boundary layer thickness and diffusive flux based on in situ measurements in coastal seas

Progress in Oceanography 144 (2016) 1–14

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Scaling relationships for diffusive boundary layer thickness and diffusive flux based on in situ measurements in coastal seas Jianing Wang a, Liang Zhao b, Renfu Fan c, Hao Wei c,⇑ a

Key Laboratory of Ocean Circulation and Waves, Institute of Oceanology, Chinese Academy of Sciences, Qingdao 266071, PR China College of Marine and Environmental Science, Tianjin University of Science and Technology, Tianjin 300457, PR China c School of Marine Science and Technology, Tianjin University, Tianjin 300072, PR China b

a r t i c l e

i n f o

Article history: Received 29 May 2015 Received in revised form 1 March 2016 Accepted 13 March 2016 Available online 17 March 2016

a b s t r a c t In situ measurements of the diffusive boundary layer (DBL) and bottom boundary layer (BBL) under different dynamic and oxygen environments in three coastal seas are analyzed. Previous scaling methods for the DBL thickness (dDBL) are summarized. Three methods that lead to consistent dimensions at both sides of the derived relationships have all been rooted in the Batchelor length scale. The method representing the Batchelor length scale as a function of flow speed (U) is found to be the most appropriate for scaling dDBL when the law of wall applies. Diffusive flux is controlled by the dynamic-forced dDBL and the difference in oxygen concentration over the DBL (DC). Values of DC could be scaled using the oxygen concentration of the BBL (CBBL) and the normalized benthic temperature. An effective method is developed for scaling the diffusive flux based on measurements of benthic temperature, salinity, U, CBBL, and the estimation of bottom roughness. The scaling of dDBL based mainly on U and the scaling of diffusive flux well fit data from the three sites, despite their distinct differences in dynamic and oxygen environments. Ó 2016 Elsevier Ltd. All rights reserved.

1. Introduction The vertical transport of dissolved substances (e.g., oxygen) across the sediment–water interface (SWI) plays an important role in pelagic and sediment ecosystems. Approaching the SWI, vertical transport is governed by turbulent eddy diffusion in the bottom boundary layer (BBL) and by molecular diffusion in the diffusive boundary layer (DBL). The DBL is a thin film of water with a height of up to a few millimeters above the sediment (Gundersen and Jørgensen, 1990). The concentration difference over the DBL and the DBL thickness (dDBL) determine the diffusive flux across the SWI. In situ measurements of dDBL are technically challenging due to the needs of delicate instruments and meticulous operations, and lacking such measurements becomes a bottleneck in estimating diffusive flux. Previous measurements of BBL and DBL revealed that dDBL is influenced by the BBL dynamics. On this basis, attempts have been made to develop a scaling method for dDBL using dynamic parameters. Laboratory measurements (e.g., Hondzo, 1998; Steinberger and Hondzo, 1999) have shown that dDBL decreases with increasing friction velocity (u⁄), and have provided an estimate of dDBL in terms of u⁄ and the Schmidt number. Two studies based on field measurements in lake water (Lorke et al., 2003; Bryant et al., 2010a) identified correlations among variations ⇑ Corresponding author. E-mail address: [email protected] (H. Wei). http://dx.doi.org/10.1016/j.pocean.2016.03.001 0079-6611/Ó 2016 Elsevier Ltd. All rights reserved.

in seiche-induced turbulence, dDBL, and the diffusive flux of dissolved oxygen, and demonstrated that the Batchelor length scale based on the dissipation rate of turbulent kinetic energy (TKE, em) in the BBL adequately describes variability in the observed dDBL. Simultaneous measurements of BBL and DBL were made in two coastal seas by Wang et al. (2012, 2013). They found that tidal flow drives the variation of dDBL, and proposed a scaling of dDBL through estimating the Batchelor length scale based mainly on flow speed (U), which can be more easily measured than turbulent parameters. The dependencies of diffusive flux on dDBL and concentration difference over the DBL have been extensively discussed in previous studies. A number of studies based on models (e.g., Brand et al., 2009) and field measurements (e.g., Lorke et al., 2003; Glud et al., 2009; Bryant et al., 2010a) have revealed the strong influence of dDBL on diffusive flux. Model simulations showed that oxygen flux considered alongside DBL thickness increased by up to 22%, as compared with flux simulated in the absence of the DBL (Kelly-Gerreyn et al., 2005). Glud et al. (2007) used a dynamic model to illustrate that diffusive flux depends more on dDBL when the time scale is hours or days rather than years. Theoretical (e.g., Higashino et al., 2004, 2008; Lorke and Peeters, 2006) and field (e.g., Brand et al., 2008; Berg et al., 2013) studies have highlighted how BBL dynamics characterized by U, u⁄, or em can affect diffusive flux through dDBL. Based on in situ measurements in the North Sea, McGinnis et al. (2014) showed that BBL turbulence

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J. Wang et al. / Progress in Oceanography 144 (2016) 1–14

forced a 25-fold variation in diffusive flux over one tidal cycle. Besides dDBL, diffusive flux is also influenced by concentration differences over the DBL, which are themselves determined by both diffusive transport processes in the water and consumption processes in the sediment. Based on field observations, Glud et al. (2003) found that seasonal variations in diffusive flux strongly depend on changes in bottom water oxygen concentrations. The oxygen flux was related to bottom water oxygen concentration (denoting oxygen supply rate) and sediment oxygen consumption rate (Bouldin, 1968). The sediment oxygen consumption was later related to the core top organic carbon concentration (Cai and Reimers, 1995) or bottom temperature (Hetland and DiMarco, 2008). Scalo et al. (2013) proposed a parameterization of oxygen concentration difference based on u⁄, sediment oxidation rate, bottom temperature, and oxygen concentration through a large-eddy simulation that reproduced field measurement in lake water (Bryant et al., 2010a). Previous studies have proposed different scaling relationships for dDBL (e.g., Hondzo, 1998; Lorke et al., 2003; Wang et al., 2013). For these relationships, dDBL is scaled using different BBL dynamic parameters, and using different values of empirical coefficients. Until now, there have been few comprehensive analyses on the influences of potential factors on diffusive flux, and the flux remains poorly quantified, especially for coastal seas. Therefore, more measurements under different oceanic environments are needed to improve scaling methods for dDBL and diffusive flux. The proper parameterizations of dDBL and diffusive flux are necessary for biophysical models that characterize the processes near the SWI. In coastal seas, energetic tidal flow further increases the challenge of making in situ observation of the DBL. On the other hand, studies on the complexity and transient characteristics of coastal seas shall lead to more robust understanding of diffusive transport around the SWI.

In this study, we report new observations in the Changjiang (Yangtze River) Estuary and the synthesis of new data with previous observations in two coastal seas: Bohai Bay and an intertidal mudflat in Huichang Bay. The three observation sites were located in the East China Sea, Bohai Sea and Yellow Sea, respectively (Fig. 1). Preliminary analyses of the two previous observations were reported by Wang et al. (2012, 2013). BBL dynamic forcings in the Changjiang Estuary, Bohai Bay, and Huichang Bay are strong, weak, and moderate, respectively; while oxygen concentrations in the water columns are low, moderate, and high, respectively. Therefore, these three observation datasets allow for the comparison of oxygen transport under different environments, and for possible development of unified scaling methods.

2. In situ measurements Measurements in the Changjiang Estuary (30.84°N, 122.66°E) were conducted from 19:00 on 17 July 2013 to 08:20 on 18 July 2013 (local time, same hereinafter) in a mean water depth of 19.6 m (Table 1). In Bohai Bay (39.05°N, 117.87°E), measurements were made from 20:00 on 24 August 2011 to 06:00 on 25 August 2011 in a mean water depth of 6.5 m (Table 1). In Huichang Bay (36.30°N, 120.65°E), measurements were made from 17:20 to 22:40 on 27 November 2010 (Table 1). In Huichang Bay, sediments were covered by seawater during half of the semidiurnal tidal cycle and the maximum water depth was 2.0 m. The sediment types at the three sites are similar, with silty clay in Bohai Bay and the Changjiang Estuary and sand–silt–clay in Huichang Bay (Chen, 1990). For the three measurements, a tripod was deployed on the seabed. Major instruments mounted on the tripod include a Unisense Mini Profiler MP4, a Nortek acoustic Doppler velocimetry (ADV), and a RBR420 conductivity-temperature-depth (CTD).

Fig. 1. Map of the study regions, with the Changjiang Estuary, Bohai Bay, and Huichang Bay highlighted using enlarged panels (right-hand side) and measurement locations denoted by solid circles. Isobaths (dashed lines) represent contours in meters.

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J. Wang et al. / Progress in Oceanography 144 (2016) 1–14 Table 1 Location, time, mean water depth, and sediment type of three measurements in different coastal seas.

Changjiang Estuary Bohai Bay Huichang Bay

Latitude/longitude

Local time

Mean Water depth

Sediment type

30.84°N/122.66°E 39.05°N/117.87°E 36.30°N/120.65°E

19:00 17 July 2013–08:20 18 July 2013 20:00 24 August 2011–06:00 25 August 2011 17:20–22:40 27 November 2010

19.6 m 6.5 m Sediment covered by seawater for half semidiurnal tidal cycle; maximum water depth 2.0 m

Silty clay Silty clay Sand–silt–clay

Profiles of oxygen concentration were measured using the Unisense Mini Profiler MP4, which was equipped with a Clark-type oxygen microsensor (OX25, Unisense A/S). The working modes of the MP4 were the same for the three sites. Each profile had a vertical resolution of 50 lm. Profile measurement started at
1–2 mm above the SWI and ended at
2–3 mm below the SWI, at the point where oxygen concentrations in the sediment reached a constant and low value. This ensured that the anoxic zone was resolved by the MP4. At each depth, after a brief 5 s pause allowing the sensor to reach equilibrium, five values were recorded at 1 Hz. The measurement of each profile took
15–30 min. We obtained 23, 19, and 11 oxygen profiles in the Changjiang Estuary, Bohai Bay, and Huichang Bay, respectively. Three-dimensional velocity in the BBL was measured by a downward-looking ADV. The ADV sampled data in continuous mode with a frequency of 32 Hz, positioned at 0.25 m above bottom (mab) in the Changjiang Estuary and 0.24 mab in Bohai Bay. In Huichang Bay, the ADV sampled data in burst mode with a frequency of 8 Hz, positioned at 0.22 mab. Each burst lasted 6 min and the interval between two bursts was 4 min. The velocity measured by ADV was used to estimate em and u⁄. Temperature (T) and salinity (S) in the BBL were measured by the RBR420 CTD with a sampling frequency of 1 Hz, positioned at 0.70 mab in the Changjiang Estuary, 0.5 mab in Bohai Bay, and 0.4 mab in Huichang Bay, respectively. 3. BBL dynamic forcing Time series of U, em, and u⁄ were obtained in the BBL of the Changjiang Estuary, Bohai Bay and Huichang Bay (Fig. 2). At the three sites, estimates of em were obtained by fitting the energy spectra of vertical velocity fluctuations (w0 ) in the inertial subrange (Fig. 3a). The energy spectrum with wave contamination removed ðU0w0 Þ was obtained by:

U0w0 ¼ Uw0 ð1  c2w Þ

ð1Þ

where Uw0 is the original energy spectrum of w0 with wave disturbance included and cw is the coherence between the pressure fluctuation (p0 ) and w0 . Values of cw were calculated via

c2w ¼

C p0 w0 C p0 w0

Up0 Uw0

;

ð2Þ

where Cp0 w0 is the cross spectrum of p0 and w0 and C⁄p0 w0 its complex conjugate, and Up0 is the energy spectrum of p0 . Differences between power spectra with and without wave contaminations were the largest in Huichang Bay, suggesting that spectra in intertidal mudflat were more easily influenced by surface waves. However, the frequencies corresponding to wave contamination were lower than those corresponding to inertial subranges; therefore, surface waves had little influence on estimates of em. Values of qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 12 2 2 u ¼ ½ ðu0 w0 Þ þ ðv 0 w0 Þ  were obtained by computing the covariance of different components of velocity fluctuations denoted by u0 , v0 , and w0 (e.g., Liu and Wei, 2007). A good correlation among U, em, and u⁄ was generally established in the Changjiang Estuary and Bohai Bay, but not in Huichang Bay. This is possibly due to

the limited measurement duration of Huichang Bay, which only enabled providing a snapshot of dynamic conditions. Regarding the near-bed turbulence, it was expected that em and u⁄ would correlate in terms of the law of wall:

em ¼

u3

jzm

;

ð3Þ

where j is the von Karman’s constant and zm is the measurement height of em relative to the bottom (zm = 0.25 mab for the Changjiang Estuary, zm = 0.24 mab for Bohai Bay, and zm = 0.22 mab for Huichang Bay). Scatter diagram of u3 =jzm versus em, including data from the three sites, showed that 90% of the ratios between u3 =jzm and em were within 0.1 and 10 (Fig. 3). This suggests that u3 jzm and em were almost in the same order of magnitude, especially for the high values of em obtained in the Changjiang Estuary and Huichang Bay. For the low values of em obtained in Bohai Bay, a possible underestimation of u⁄ resulted in em values that were on average larger than u3 jzm The law of wall was well satisfied with a total correlation coefficient (r) of 0.81 and p-value (probability for testing the hypothesis of no correlation) of 0.00. The medians of em obtained from the Changjiang Estuary, Huichang Bay, and Bohai Bay were 1.2  105, 8.2  106, and 1.1  106 W kg1, respectively, indicating different BBL dynamics. The ranges, means, and standard deviations of U, em, and u⁄ (Table 2) support the theory that the Changjiang Estuary, Huichang Bay, and Bohai Bay are characterized by strong, moderate, and weak dynamic forcings, respectively. The establishment of the law of wall suggests that the vertical distribution of the horizontal flow speed with height above bottom was logarithmic, that is:

UðzÞ ¼

u

j

lnðz=z0 Þ;

ð4Þ

where z0 is bottom roughness length and z is the height above the sediment. From (4), bottom roughness length can be calculated via: jU

z0 ¼ zm e u :

ð5Þ

Data corresponding to the time when the ratio of u3 jzm versus em was between 0.1 and 10 were used to calculate z0. Mean values of z0 in the Changjiang Estuary, Bohai Bay, and Huichang Bay were 2.62, 0.62, and 30 mm, respectively. Mean values of z0 were inversely proportional to the distances between measurement sites and the shore (Fig. 1), which was consistent with the fact that the height of terrain roughness is usually larger when a study site is closer to the shore (Soulsby, 1983). 4. DBL thickness and diffusive flux Following Wang et al. (2013), we estimated dDBL and calculated the diffusive flux from the water (Jwater) and sediment (Jsediment) sides in the Changjiang Estuary. We defined dDBL as the distance between the bottom of the BBL and the SWI (e.g., Gundersen and Jørgensen, 1990), and the bottom of the BBL as the bottom of the region where oxygen concentration is linearly distributed owing to eddy diffusion. Three methods were combined to estimate the location of the SWI: defining it as the bottom of the region with linear decrease of oxygen concentration (Steinberger and Hondzo,

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J. Wang et al. / Progress in Oceanography 144 (2016) 1–14

Fig. 2. BBL dynamic conditions in: (a) Changjiang Estuary, (b) Bohai Bay, and (c) Huichang Bay. For each site, time series of flow speed (U), turbulent kinetic energy dissipation rate (em), and friction velocity (u⁄) are shown. Black and gray lines denote original values and their 10-points moving averages, respectively. Black squares denote when oxygen profiles were observed.

1999), the kink point in the concentration slope (Røy et al., 2004), and the position where the variance of oxygen concentration decreases drastically (Müller et al., 2002). The diffusive flux describes the molecular diffusive transport of oxygen supplied to sediment, but not the total oxygen uptake. Oxygen fluxes induced by advection, bioturbation and faunal activity were not considered here. Values of Jwater were calculated according to the Fick’s first law:

J water ¼ D

C BBL  C SWI ; dDBL

ð6Þ

where D is the molecular diffusivity of oxygen, and CBBL and CSWI are oxygen concentrations in the BBL and at the SWI, respectively. The values of D describe physical property of oxygen that is mainly determined by seawater T and S. Ramsing and Gundersen (1994)

provided a table that includes the values of D at various temperatures and salinities. We obtained the values of D in this table according to our measured T and S, shown in Fig. 4. In the Changjiang Estuary and Bohai Bay, high values of T corresponded to low values of S, and vice versa; while in Huichang Bay, variations in T and S were positively correlated. The different relationships between T and S at the three sites were possibly caused by the different water mass properties. Ranges in the values of T were 20.1– 22.1 °C in the Changjiang Estuary, 26.5–26.6 °C in Bohai Bay, and 9.9–11.4 °C in Huichang Bay. Ranges in the values of S were 32.03–33.75 psu in the Changjiang Estuary, 28.10–28.36 psu in Bohai Bay, and 33.76–34.97 psu in Huichang Bay. The small ranges in T and S resulted in low variability in the values of D: 1.96– 2.02  109 m2 s1 in the Changjiang Estuary, 2.39  109 m2 s1 in Bohai Bay, and 1.47–1.51  109 m2 s1 in Huichang Bay.

J. Wang et al. / Progress in Oceanography 144 (2016) 1–14

Fig. 3. (a) Energy spectra of vertical velocity fluctuations with wave disturbance removed (solid lines) and the corresponding original spectra with wave disturbance included (dashed lines). The black sloping line denotes the slope of a theoretical spectrum in the inertial subrange. Error bars with 95% confidence intervals are indicated. Spectra are computed for velocity time series over a segment denoted by vertical dash-dotted lines shown in Fig. 2. (b) Scatter diagram of u3 =jm versus the measured turbulent kinetic energy dissipation rate (em), with straight lines depicting the 1:10, 1:1 and 10:1 ratios and dashed lines depicting the median of em at each site. The correlation coefficient (r) and p-value are denoted. Blue, orange, and red colors denote data from the Changjiang Estuary, Bohai Bay, and Huichang Bay, respectively. Symbols with black edges denote the availability of corresponding observation of oxygen profiles.

Values of Jsediment were calculated by integrating oxygen consumption and the temporal changes of oxygen content over the sediment oxic zone using the expression:

Z J sediment ¼ 0

zmax

Z Rs dz þ 0

zmax

@C s dz; @t

ð7Þ

where Rs is the rate of oxygen consumption in the sediment, Cs is oxygen concentration in the sediment, and zmax is the oxygen penetration depth (i.e., the thickness of the sediment oxic zone; Bryant et al., 2010a,b). Values of Rs were obtained from the PROFILE model (Berg et al., 1998) that defined several zones with constant Rs through applying least-squares fit to the observed oxygen profiles. Fig. 5 shows the total 23 observed oxygen profiles and the corresponding model fits in the Changjiang Estuary. Total of 19 profiles in Bohai Bay and total of 11 profiles in Huichang Bay were displayed in Wang et al. (2013, their Figs. 5 and 7). The vertical distributions of the oxygen profiles from the three sites followed similar patterns. Oxygen concentrations were nearly uniform in the BBL and linearly decreased toward the SWI in the DBL. The concen-

5

tration slopes in the upper sediment region were smaller than those in the DBL, reflecting smaller diffusivity in the upper sediment than that in the water (Røy et al., 2004). For all the three sites, the PROFILE model well simulated the observed oxygen distributions in the DBL and the sediments with r2 higher than 0.99. For each of the profiles, the depth-integrated temporal change of oxygen concentration in the sediment was less than 4% of the depth-integrated oxygen consumption, suggesting a quasisteady-state condition. The mean discrepancies between Jwater and Jsediment, measured by |Jwater–Jsediment|/Jwater  100%, were 7.7% in the Changjiang Estuary, 2.6% in Bohai Bay, and 2.4% in Huichang Bay. This suggests that Jwater was not significantly different from Jsediment. Therefore, the final diffusive flux (Javg) was obtained by averaging Jwater and Jsediment. Table 3 lists the values of dDBL, Jwater, Rz R zmax s Rs dz; 0 max @C dz, Jsediment, Javg, and zmax in the Changjiang Estu0 @t ary. The tables listing the same information of Bohai Bay and Huichang Bay were given in Wang et al. (2013, their Tables 2 and 3). Fig. 6 shows time-depth variations of the oxygen concentration near the SWI for each of three sites, with black and white lines depicting dDBL and zmax, respectively. Table 2 lists the ranges, means, and standard deviations of dDBL, Javg, CBBL, and zmax at the three sites. The magnitude and variability of oxygen concentration in the BBL were different. The ranges in CBBL were 2.5–4.0 mg L1 in the Changjiang Estuary, 4.6–5.0 mg L1 in Bohai Bay, and 8.0– 8.5 mg L1 in Huichang Bay, corresponding to low-, moderate-, and high-oxygen environments, respectively. Values of zmax were positively correlated with CBBL, with mean values being the smallest in the Changjiang Estuary (1.41 mm), rising to 1.48 mm in Bohai Bay and 2.50 mm in Huichang Bay. Values of dDBL were 0.10–0.35 mm in the Changjiang Estuary, 0.10–0.65 mm in Bohai Bay, and 0.10–0.35 mm in Huichang Bay, with mean values of 0.22, 0.30, and 0.25 mm, respectively. In the Changjiang Estuary, Javg ranged between 8.2 and 29.9 mmol m2 d1 and had the smallest mean (20.2 mmol m2 d1) and variability (standard deviation = 5.8 mmol m2 d1). In Bohai Bay, Javg ranged between 7.8 and 54.6 mmol m2 d1, with a mean magnitude of 21.2 mmol m2 d1 and a standard deviation of 10.6 mmol m2 d1. In Huichang Bay, Javg ranged between 15.4 and 53.6 mmol m2 d1 and had the largest observed mean (25.3 mmol m2 d1) and variability (10.9 mmol m2 d1). Fig. 7 shows the vertical distributions of oxygen concentration standard deviations (roxygen) in three coastal waters. Table 2 lists the means and standard deviations of roxygen in the BBL, DBL, and the sediment, respectively. At all the three sites, roxygen in the BBL was on average smaller than that in the DBL. In the BBL, strong turbulence mixed the oxygen concentration to nearly uniform; while in the DBL, turbulent eddy diffusion was damped and molecular diffusion became the controlling process for oxygen transport. As a result, the diffusion intensity decreased, leading to increases in roxygen from the BBL to the DBL (Gundersen and Jørgensen, 1990). From the SWI to the sediment, roxygen decreased at all three sites, especially in the Changjiang Estuary and Huichang Bay where roxygen in the sediment was on average one order of magnitude smaller than that in the DBL. This was in part due to the decreasing oxygen concentration, but mostly resulted from the gradual decrease of the influence of diffusive transport in the DBL (Røy et al., 2004). On this basis, the point where variance of oxygen concentration decreases dramatically can be identified as the SWI. A similar vertical distribution of roxygen was obtained in a laboratory experiment (Røy et al., 2004), and our results are the first to verify their finding using in situ measurements. At the three sites, we found that the average values of roxygen over the BBL, DBL, and sediment were all inversely proportional to the intensity of BBL turbulence. Weak dynamic forcing in Bohai Bay corresponded to large mean roxygen, whereas strong dynamic forcing in the Changjiang

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J. Wang et al. / Progress in Oceanography 144 (2016) 1–14

Table 2 Summary of BBL and DBL measurements in three coastal seasa. Changjiang Estuary

Bohai Bay

Huichang Bay

Range Mean ± SDb

0.002–0.383 0.119 ± 0.067

0.030–0.082 0.058 ± 0.018

0.011–0.126 0.040 ± 0.034

em (W kg1)

Range Mean ± SD

1.9  107–2.2  104 1.2  105 ± 3.0  105

1.7  107–5.7  106 1.1  106 ± 1.9  106

2.8  106–1.4  105 8.2  106 ± 5.0  106

u⁄ (m s1)

Range Mean ± SD

0.003–0.030 0.011 ± 0.005

0.001–0.009 0.004 ± 0.002

0.006–0.013 0.008 ± 0.002

CBBL (mg L1)

Range Mean ± SD

2.5–4.0 3.0 ± 0.4

4.6–5.0 4.8 ± 0.1

8.0–8.5 8.2 ± 0.2

zmax (mm)

Range Mean ± SD

0.50–2.70 1.41 ± 0.45

1.10–2.00 1.48 ± 0.27

1.75–2.95 2.50 ± 0.44

dDBL (mm)

Range Mean ± SD

0.10–0.35 0.22 ± 0.07

0.10–0.65 0.30 ± 0.13

0.10–0.35 0.25 ± 0.08

Javg (mmol m2 d1)

Range Mean ± SD

8.2–29.9 20.2 ± 5.8

7.8–54.6 21.2 ± 10.6

15.4–53.6 25.3 ± 10.9

roxygen (mg L1)

Mean ± SD in the BBL Mean ± SD in the DBL Mean ± SD in the sediment

3.5  104 ± 9.4  104 3.8  104 ± 6.7  104 1.0  105 ± 9.6  106

9.0  104 ± 1.1  103 1.2  103 ± 2.0  103 4.5  104 ± 1.2  103

4.2  104 ± 2.7  104 7.7  104 ± 6.8  103 5.6  105 ± 4.9  105

Benthic temperature (°C)

Range

20.1–22.1

26.5–26.6

9.9–11.4

U (m s

a b

1

)

Benthic salinity (psu)

Range

32.03–33.75

28.10–28.36

33.76–34.97

D (m2 s1)

Range

1.96–2.02  109

2.39  109

1.47–1.51  109

BBL = bottom boundary layer, DBL = diffusive boundary layer. SD = standard deviation.

Fig. 4. Time series of temperature (T) and salinity (S) in the BBL of (a) Changjiang Estuary, (b) Bohai Bay, and (c) Huichang Bay. Black and gray lines denote original values and their 10-point moving averages. Black squares denote when oxygen profiles were observed.

J. Wang et al. / Progress in Oceanography 144 (2016) 1–14

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Fig. 5. Twenty-three oxygen concentrations (Coxygen) profiles for the Changjiang Estuary based on observations (black circles), model fitting (red lines), and modeled oxygen consumption rate Roxygen (blue step lines).

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J. Wang et al. / Progress in Oceanography 144 (2016) 1–14

Table 3 Characteristics of oxygen profiles in the Changjiang Estuary.a Profile number

Time (h:min)

dDBL (mm)

Jwater (mmol m2 d1)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23

19:02 19:52 21:20 21:53 22:15 22:35 22:53 23:20 23:50 00:21 00:45 01:10 04:43 05:05 05:30 05:50 06:22 06:45 07:05 07:25 07:45 08:02 08:20

0.15 0.15 0.30 0.25 0.30 0.30 0.15 0.10 0.35 0.25 0.15 0.15 0.30 0.20 0.20 0.20 0.15 0.25 0.20 0.15 0.15 0.30 0.25

22.2 20.3 24.8 14.4 14.1 11.9 19.9 7.9 16.2 20.5 15.3 21.3 18.5 26.6 31.3 16.3 26.1 19.5 30.8 19.9 29.3 26.9 29.7

0.22 0.07

21.0 6.4

Mean SDb

R zmax

R zmax

@C s 0 @t dz (mmol m2 d1)

Jsediment (mmol m2 d1)

Javg (mmol m2 d1)

zmax (mm)

16.7 19.3 21.4 14.0 14.6 11.8 17.2 8.5 15.1 17.9 14.5 19.3 19.1 27.1 29.0 15.7 21.4 20.8 26.2 19.8 27.9 24.4 25.7

0.3 0.0 0.6 0.1 0.2 0.4 0.0 0.2 0.3 0.0 0.1 0.1 0.3 0.5 0.2 0.1 0.0 0.2 0.1 0.2 0.2

16.7 19.6 21.4 13.4 14.5 11.6 16.8 8.5 15.3 17.6 14.5 19.4 19.2 26.8 28.5 15.5 21.3 20.8 26.4 19.9 27.7 24.2 25.7

19.4 19.9 23.1 13.9 14.3 11.8 18.3 8.2 15.8 19.0 14.9 20.3 18.8 26.7 29.9 15.9 23.7 20.2 28.6 19.9 28.5 25.5 27.7

1.35 1.15 0.50 1.15 1.25 1.30 1.55 1.60 2.70 1.70 2.50 1.65 1.05 1.30 1.25 1.45 1.25 1.30 1.15 1.25 1.25 1.40 1.35

19.4 5.4

0.1 0.2

19.4 5.4

20.2 5.8

1.41 0.45

Rdz (mmol m2 d1) 0

Rz a dDBL = diffusive boundary layer (DBL) thickness, Jwater = oxygen diffusive flux calculated from water-side, Jsediment = sediment-side, 0 max Rdz = depth integrated oxygen Rz R zmax R zmax @C s @C s s consumption rate, 0 max @C dz = temporal change (J = Rdz þ dz), J = (J + J )/2 = the average diffusive flux, z sediment avg water sediment max = penetration depth. Values of @t 0 0 @t @t were obtained using the values of the two adjacent profiles. b SD = standard deviation.

Estuary corresponded to small mean roxygen. Scalo et al. (2012) noted a similar response of roxygen to different turbulent intensities in large-eddy simulation results. Here we provided the first observed evidence from field measurements. 5. Scaling DBL thickness and diffusive flux 5.1. Scaling DBL thickness with BBL dynamics Our results showed that variations in dDBL were inversely proportional to BBL dynamic parameters (i.e., U, em, u⁄; Fig. 8). Increases in U, em, and u⁄ corresponded to decreases in dDBL, and vice versa. The strong, moderate, and weak BBL dynamics were consistent with the small (0.22 mm), medium (0.25 mm), and large (0.30 mm) mean values of dDBL in the Changjiang Estuary, Huichang Bay, and Bohai Bay, respectively. This suggests that dDBL is strongly influenced and can thus be scaled by BBL dynamics. As discussed, numerous dDBL scaling methods using BBL dynamics have been proposed; however, these methods differ in dynamic parameters and empirical fitting coefficients and can be classified into the following four categories. (a) Function of viscous length scale (m/u⁄) and Schmidt number Under the assumption that streamwise vortices control oxygen transfer near the SWI, Hondzo (1998) provided an estimate of dDBL as a function of viscous length scale and Schmidt number:

LSc ¼ c

m u

Sc1=2 ;

ð8Þ

where c is an empirical fitting coefficient, m is kinematic viscosity, and Sc = m/D is the Schmidt number. Through least-squares fitting to laboratory experimental data, Hondzo (1998) obtained a linear regression relationship b = 2  102 u ⁄ Sc1/2, where b = D/dDBL is a mass transfer coefficient. Assuming dDBL as the height above the

SWI where advection balances vertical diffusion, Steinberger and Hondzo (1999) obtained a similar expression:

LSc ¼ ð19:5  5:5Þ

m u

Sc1=3 ;

ð9Þ

albeit with an exponent of 1/3 instead of 1/2 for Sc. Lorke and Peeters (2006) speculated that low level turbulence leads to intermittency and anisotropy of turbulence and that interfacial exchange depends more strongly on D, resulting in the increasing exponent of Sc. (b) Batchelor length scale as a function of TKE dissipation rate Based on a numerical model, Hearn and Robson (2000) suggested that dDBL can be scaled using the Batchelor length scale:

mD2 LB ¼ 2p e

!1=4 ;

ð10Þ

where LB characterizes the smallest length scales of turbulent fluctuations in scalar concentrations. Fluctuations with length scales smaller than LB are diffused by molecular process (Batchelor, 1959). Later field observation from a lake (Lorke et al., 2003) demonstrated that dDBL can be described well using LB obtained from the TKE dissipation rate (er) at a reference height (zr) of 10 mm above the seabed. The values of er at zr = 10 mm is extrapolated by using em directly measured at 0.5 mab based on the law of wall (er = zmem/zr). Wang et al. (2013) provided an expression of the Batchelor length scale at zr as:

 LBr ¼ 2p

zr zm

1=4

mD2 em

!1=4 :

ð11Þ

However, LBr had a low correlation with observed dDBL from Bohai Bay and Huichang Bay, and hence was less accurate for scaling dDBL.

J. Wang et al. / Progress in Oceanography 144 (2016) 1–14

9

Fig. 6. Time-depth variations of oxygen concentration (Coxygen) in: (a) Changjiang Estuary, (b) Bohai Bay, and (c) Huichang Bay. Black and white lines denote the DBL thickness and the penetration depth, respectively.

(c) Batchelor length scale as a function of flow speed Next, Wang et al. (2013) sought to parameterize the Batchelor length scale with more easily measured physical quantities. Based on the law of wall (Eq. (3)), an alternative estimate of the Batchelor length scale as a function of u⁄, denoted as L⁄Br, can be given as:

 1=4 LBr ¼ 2p zr jmD2 u3 : 

ð12Þ

Based on a logarithmic vertical profile of horizontal flow speed (Eq. (4)), Wang et al. (2013) also derived an alternative estimate of the Batchelor length scale (L# Br) as a function of U: 3 1=4

2 3 2 L# Br ¼ 2pfzr j mD U ½lnðzm =z0 Þ g

L# Br

:

ð13Þ

had a high correlation with observed dDBL from Bohai Bay and Huichang Bay and hence more accurately scaled dDBL. L# Br

allows the estimate of the Batchelor length scale based on flow speed which is more easily measured than turbulent quantities (e.g., em and u⁄). (d) Other scaling methods Bases on the results of a laboratory experiment, Hondzo et al. (2005) parameterized dDBL using the Reynolds number (Re; i.e., dDBL = 134Re0.6). Fitting composite laboratory results and in situ data from Aarhus Bay, Glud et al. (2007) obtained a relationship between U and dDBL (dDBL = 3.0U0.96). Both methods well fit the corresponding data; however, the dimensions on both sides of the derived relationships are not consistent, and this puts limitations on their general applications. Methods b and c both scale dDBL with the Batchelor length scale, while Method a can also be related to the Batchelor length scale through a simple conversion (Lorke and Peeters, 2006). The Kolmogorov length is defined as:

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J. Wang et al. / Progress in Oceanography 144 (2016) 1–14

Fig. 7. Vertical distributions of standard deviations of oxygen concentration (roxygen) in: (a) Changjiang Estuary, (b) Bohai Bay, and (c) Huichang Bay. Black solid circles denote observed values and blue lines show their medians at the same depths. Values of roxygen in the DBL are denoted in red.

Fig. 8. Time series of DBL thickness (dDBL, gray bars), flow speed (U, black), turbulent kinetic energy dissipation rate (em, blue), and friction velocity (u⁄, red). Axes for U, em, and u⁄ are reversed.

 3 1=4 m LK ¼ 2p ;

ð14Þ

e

where LK describes the length at which turbulent stress becomes damped and molecular viscous stress becomes important. Therefore, LK can be taken as the lower bound of the region where the law of wall is established. By applying the law of wall at a height of LK, i.e., setting zm = LK in Eq. (3), and then substituting it in Eq. (10) for the Batchelor length scale, one yields:

LSc ¼ LB ¼ ð2pÞ4=3 j1=3

m u

Sc1=2  8:61

m u

Sc1=2 ;

ð15Þ

which agrees with Eq. (8). Methods a, b, and c, which are all rooted in the Batchelor length scale, differ in two main aspects. First, the Batchelor length scale is described in different terms (em, u⁄, and U, respectively). Second,

the reference heights for the Batchelor length scale are different. Eqs. (11), (12), and (13) define the Batchelor length scale at a fixed height zr with time, whereas Eq. (15) defines it at a time-varying height LK. Estimates of dDBL with u⁄ and U require the validity of the law of wall. Therefore, the estimate of dDBL with em (Eq. (11)) is recommended when the law of wall does not apply, for example, when the BBL turbulence is controlled by convective mixing or there is an evident phase lag between em and U in the BBL (Lorke et al., 2003). The law of wall was satisfied for the observations at each of our study sites, especially when the oxygen profiles were observed (Fig. 3b). Therefore, we evaluated the relative accuracies in the scaling of dDBL using four estimates of the Batchelor length scale: LSc (Eq. (15)), LBr, L⁄Br, and L# Br. Fig. 9 shows the scatter diagrams of dDBL versus LSc, LBr, L⁄Br, and L# Br. For each scaling method, a linear regression with zero interception was obtained through least-

J. Wang et al. / Progress in Oceanography 144 (2016) 1–14

11

Fig. 9. Scatter diagrams of observed DBL thickness (dDBL) versus the Batchelor length scale calculated as: a) LSc according to (15), b) LBr according to (11), c) L⁄Br according to ⁄ # (12), and d) L# Br according to (13). The reference height for calculating LBr, LBr and LBr is 10 mm. Straight lines depict the linear regression between the Batchelor length scale and dDBL obtained from least-squares fitting, with the corresponding relationship, correlation coefficient (r), and p-value for the regression fit shown. An error bar with a 95% confidence interval is shown in each panel.

squares fitting of all data from the three sites. The derived linear relationships were dDBL = 2.5LSc with r = 0.56, dDBL = 2.5LBr with r = 0.61, dDBL = 1.9L⁄Br with r = 0.56, and dDBL = 3.7L# Br with r = 0.81. LSc and L⁄Br had poor correlations with dDBL, while LBr was moderately correlated with dDBL. In contrast, L# Br had a strong correlation with dDBL at all three sites. Estimates of the Batchelor length scale with u⁄, em, and U had a low, moderate, and high accuracy in representing dDBL, which likely reflects the measurement accuracies of u⁄, em, and U. Values of u⁄ were calculated directly using high frequency velocity fluctuations, which have large uncertainties. Values of em are estimated through averaging the energy spectral density of velocity fluctuations over the inertial subrange, which reduces measurement error of velocity fluctuations. Compared with high-order turbulent quantities (e.g., u⁄ and em), U can be more easily and accurately measured. Furthermore, the relationship dDBL = 3.7L# Br well fit the results from all three sites. This suggests that L# Br is simple and effective. On this basis, dDBL is recommended to be parameterized in terms of U, according to Eq. (13), when the law of wall applies. 5.2. Scaling diffusive flux According to the Fick’s first law, diffusive flux across the SWI is related to D, dDBL, and oxygen concentration difference over the DBL (DC). The DC is further determined by oxygen concentrations in the BBL (CBBL) and at the SWI (CSWI). The CSWI is influenced by both the diffusive transport from the water that supplies oxygen, and sediment mineralization process that consumes oxygen. Many previous studies on the influencing factors of diffusive flux put more weight on biochemical processes in the sediment (e.g., Glud et al., 2003). In this study, we took the opposite approach, with an emphasis on physical processes in the water. We simply specified the oxygen consumption to be positively proportional to 2T/Tm, where Tm is the mean temperature of each dataset and T/Tm denotes the normalized benthic temperature. We examined the dependency of Javg on potential influencing factors. The Javg values were considered as a function of nondynamic (CBBL, 2T/Tm, DC, and dDBL; Fig. 10a–d) and dynamic factors (em, u⁄, and U; Fig. 10e–g). With respect to non-dynamic factors, increases in CBBL, 2T/Tm, and their resultant DC correspond to

increase in Javg, while increase in dDBL corresponds to decrease in Javg for all data. However, the r and p values of Javg versus dDBL, DC, CBBL, and 2T/Tm at each site differed significantly (Table 4). In the Changjiang Estuary, Javg showed a correspondence (r greater than 0.5 and p less than 0.05) with CBBL, 2T/Tm, and DC, but little correspondence with dDBL. This result suggests that Javg was mainly determined by DC, in part because CBBL and 2T/Tm had higher variability than dDBL. In contrast, dDBL was the first decisive factor of Javg for Bohai Bay, which can be attributed to high variability in dDBL and low variability in CBBL and 2T/Tm. In Huichang Bay, these factors had similar levels of variability, resulted in similar contributions to Javg. Dynamic factors influence Javg mainly through dDBL. In general, Javg was more highly correlated with U than with em and u⁄, likely due to the higher measurement accuracy of U. The results clearly show a relationship between U and Javg in Bohai Bay and Huichang Bay, with dDBL as the decisive factor. In the Changjiang Estuary, although the correlation between dDBL and Javg was poor, the value of r between Javg and U was relatively high and its sign was positive and negative for small and large values of U, respectively. This can be attributed to a positive relationship between dDBL and DC in the Changjiang Estuary (Fig. 10h). With increasing U, decreasing dDBL caused increase in Javg but decrease in DC, which also acted to reduce Javg. This leads to the opposite contributions of small and large values of U to Javg. In other words, increase in dDBL can cause both increase and decrease in Javg. This is the other reason for a poor correlation between dDBL and Javg in the Changjiang Estuary. From the above analyses we can conclude that: (1) the ranges of variability in CBBL, 2T/Tm, and dDBL determine the relative importance of dDBL and DC to Javg; (2) increase of dDBL can lead to both increase and decrease in Javg; and (3) U provides a more accurate scaling of Javg, as compared with em and u⁄. The calculation of Javg requires estimates of D, dDBL, and DC. Among these, D is mainly determined by benthic T and S, which can be easily measured; dDBL can be scaled by BBL dynamic conditions; and DC remains to be determined. As previously discussed, DC should be proportional to CBBL and 2T/Tm, which denote oxygen supply and consumption, respectively. We proposed a scaling relationship for DC (DCmodel):

DC model ¼ fC BBL 2T=Tm ;

ð16Þ

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J. Wang et al. / Progress in Oceanography 144 (2016) 1–14

Fig. 10. Scatter diagrams of diffusive flux (Javg) versus: (a) oxygen concentration in the BBL (CBBL), (b) normalized benthic temperature (2T/Tm), (c) oxygen concentration difference over the DBL (DC), (d) DBL thickness (dDBL), (e) turbulent kinetic energy dissipation rate (em), (f) friction velocity (u⁄), and (g) flow speed (U). (h) Scatter diagram of DC versus dDBL. In each panel, the straight line depicts the linear regression obtained from least-squares fitting, with the correlation coefficient (r) for the regression fit shown. The vertical line in panel (g) serves as a guide to separate large and small values of U.

where f is an empirical fitting coefficient. By substituting DC (CBBL–CSWI) in Eq. (6) with DCmodel and by substituting dDBL in Eq. (6) with 3.7L# Br, an estimate of diffusive flux (Jmodel) can be obtained by:

J model ¼

fDC BBL 2T=T m : 3:7L# Br

ð17Þ

The least-squares fitting of Jmodel to the observed Javg yielded f = 0.10.

13

J. Wang et al. / Progress in Oceanography 144 (2016) 1–14 Table 4 Correlation coefficients and the p-valuesa between diffusive flux Javg and potential influencing factors.

Javg vs. CBBL Javg vs. 2T/Tm Javg vs. dDBL Javg vs. DC Javg vs. log10(e) Javg vs. u⁄ Javg vs. U (small) Javg vs. U (large) dDBL vs. DC a

Changjiang Estuary

Bohai Bay

Huichang Bay

Total

0.59 (0.00) 0.55 (0.01) 0.04 (0.85) 0.67 (0.00) 0.26 (0.24) 0.26 (0.22) 0.75 (0.00) 0.83 (0.00) 0.67 (0.00)

0.01 (0.98) 0.01 (0.98) 0.49 (0.03) 0.34 (0.15) 0.37 (0.12) 0.46 (0.05) 0.49 (0.03)

0.66 (0.03) 0.48 (0.13) 0.63 (0.04) 0.52 (0.10) 0.08 (0.81) 0.14 (0.69) 0.81 (0.00)

0.48 (0.04)

0.29 (0.38)

0.26 (0.06) 0.34 (0.01) 0.36 (0.01) 0.50 (0.00) 0.13 (0.34) 0.11 (0.45) 0.38 (0.01) 0.86 (0.00) 0.38 (0.00)

p-values (denoted in brackets) = probability for testing the hypothesis of no correlation.

Fig. 11. Time series of observed diffusive flux (Javg, gray circles and lines), and modeled diffusive flux (Jmodel, black solid lines) as function of (a) L# Br and (b) dDBL. The corresponding regression, correlation coefficient (r), and p-value are denoted. The 95% confidence intervals are indicated by black dashed lines.

The time series of observed and modeled diffusive flux were compared for the three sites (Fig. 11). The r value between Jmodel and observed Javg was 0.45, increasing to 0.54 when Jmodel was directly parameterized with observed dDBL instead of L# Br. The uncertainty in the scaling was partly due to that in the scaling of dDBL. The values of Jmodel generally captured the variations and magnitudes of observed Javg at the three sites; therefore, Eq. (17) can be used to scale Javg. The results show that Jmodel provides a simple and effective scaling method of diffusive flux based on measurements of benthic T, S, CBBL, U, and the estimation of z0. 6. Summary and conclusions In situ measurements of the DBL and BBL in three coastal seas with different bottom boundary hydrodynamics and oxygen environments were analyzed. The BBL dynamic forcings in the Changjiang Estuary, Huichang Bay, and Bohai Bay are strong, moderate, and weak, while the oxygen concentrations in the water columns are low, high, and moderate, respectively. Therefore, synthesis of the three datasets provides a good opportunity to develop unified parameterizations of dDBL and diffusive flux that can be applied to diverse scenarios. Values of dDBL are strongly influenced by BBL dynamics. We summarized previous scaling methods for dDBL. The methods that lead to consistent dimensions at both sides of the derived relationships have all been rooted in the Batchelor length scale, though based on different parameters such as em, u⁄, and U. When the law of wall is not satisfied in the BBL, the Batchelor length scale as a function of em (LBr, Eq. (11)) is recommended to scale dDBL. However, when the law of wall is satisfied in the BBL, the Batchelor

length scale as a function of U (L# Br, Eq. (13)) is recommended. Values of L# Br can be easily derived using U, m, D, and the estimation of z0. The resulting L# Br well fit all three datasets, despites their distinctly different dynamic and oxygen environments. The dependencies of diffusive flux on the potential influencing factors were examined. The results showed that Javg is controlled by DC and dDBL. The DC is further determined by CBBL and normalized benthic temperature (2T/Tm), which represent oxygen supply and consumption, respectively. Their relative importance to Javg depends on the magnitudes of their variability. Dynamic factors mainly influence Javg through dDBL. A simple scaling relationship for Javg using measurements of benthic T, S, U, CBBL, and the estimation of z0 was proposed. This scaling well captured the variations and magnitudes of Javg, and can be applied in regions with similar sediment characteristics as our three study sites. The contributions of this study mainly include: (1) the addition of new in situ measurement of DBL under more energetic dynamic conditions in coastal waters; (2) a summary of scaling methods for dDBL and a discussion of their applicability in different scenarios; (3) a proposed parameterization of diffusive flux based on easily derived quantities; and (4) dDBL scaling based mainly on velocity and diffusive flux scaling that well fit data from the three study sites with distinct dynamic and oxygen environments. Although this study focused on the diffusive transport of oxygen around the SWI, the knowledge gained regarding scaling relationships for dDBL and diffusive flux can be more broadly applied to other dissolved substances. In future studies, we hope that the scaling of diffusive flux can be achieved through quantifying the sediment biochemical processes and water physical processes simultaneously.

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J. Wang et al. / Progress in Oceanography 144 (2016) 1–14

Acknowledgements We thank two anonymous reviewers and the editor for helpful comments. This study is supported by the National Natural Science Foundation of China (Grant Nos. 41406015, 41376112 and 41276016), the Strategic Priority Research Program of the Chinese Academy of Sciences (Grant Nos. XDA11020305 and XDA11010204) and the National Basic Research Program of China (973 Program, Grant No. 2011CB403606).

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