Listening to air–water gas exchange in running waters

Abstract

Air–water gas exchange velocities (k) are critical components of many biogeochemical and ecological process studies in aquatic systems. However, their high spatiotemporal variability is difficult to capture with traditional methods, especially in turbulent flow. Here, we investigate the potential of sound spectral analysis to infer k in running waters, based on the rationale that both turbulence and entrained bubbles drive gas exchange and cause a characteristic sound. We explored the relationship between k and sound spectral properties using laboratory experiments and field observations under a wide range of turbulence and bubble conditions. We estimated k using flux chamber measurements of CO₂ exchange and recorded sound above and below the water surface by microphones and hydrophones, respectively. We found a strong influence of turbulence and bubbles on sound pressure levels (SPLs) at octave bands of 31.5 Hz and 1000 Hz, respectively. The difference in SPLs at these bands and background noise bands showed a linear correlation with k both in the laboratory (R² = 0.93–0.99) and in the field (median R² = 0.42–0.90). Underwater sound indices outperformed aerial sound indices in general, and indices based on hydraulic parameters in particular, in turbulent and bubbly surface flow. The results highlight the unique potential of acoustic techniques to predict k, isolate mechanisms, and improve the spatiotemporal coverage of k estimates in bubbly flow.

Running waters provide fundamental services to humans such as drinking water, fisheries, nutrient removal, and greenhouse gas regulation (Aylward et al. 2005). Many of the underlying ecological and biogeochemical processes are limited by rates of gas exchange across the air–water interface. To accurately estimate air–water gas exchange is challenging but essential for our ability to understand key functions of running waters.

Whole-ecosystem rates of ecological or biogeochemical processes in aquatic ecosystems can be estimated by mass balance models using dissolved gases. A critical component of these models is the diffusive gas flux across the air–water interface (McCutchan et al. 1998; Laursen and Seitzinger 2005; Aristegi et al. 2009), defined as the product of the gas concentration gradient across the air–water interface, and the gas exchange velocity k. New sensor and logger technology is now widely applied to measure aqueous gas concentrations continuously at specific sites or by spot sampling at high spatial resolutions (Bernhardt et al. 2017; Crawford et al. 2017). Yet, this technology can only be used to its full potential to estimate key processes if k is measured or modeled (e.g., Appling et al. 2018) at similar resolutions as gas concentrations. This is rarely the case, implying an urgent need for improved methods to estimate k in running waters, especially in smaller high-turbulence systems where both mean rates and variability may be particularly high (Tobias et al. 2009; Wallin et al. 2011; Schelker et al. 2016) and where k is more difficult to model from diel oxygen data (as in Appling et al. 2018).

Air–water gas exchange rates are controlled by dissipation of near-surface turbulence which drives interfacial exchange (Lamont and Scott 1970) and are further enhanced by bubble-mediated exchange (Cirpka et al. 1993; Woolf 1993). Bubble-mediated gas exchange is an important but poorly quantified component of k in running waters (Ulseth et al. 2019). Bubble contributions increase with channel slope (Hall et al. 2012; Hall and Madinger 2018) and can dominate over interfacial exchange in cascading channels with slopes ≥ 1% (Cirpka et al. 1993; Chanson 1995). Such slopes are widespread across the earth (Larsen et al. 2014) but steeper systems are currently not well represented in global estimates of k in running waters (Raymond et al. 2013).

Estimating k is labor extensive and often associated with large errors, especially in bubbly flow. In running waters, k is usually measured by means of volatile tracer gas injection experiments (Wanninkhof et al. 1990; Wallin et al. 2011) or gas flux chambers (Billet and Moore 2007; Sand-Jensen and Staehr 2012; Lorke et al. 2015). Large fieldwork efforts limit these methods to a small number of locations and sampling occasions. Methods are also limited in their applicability across different surface flow types. In steep bubbly flow, gas flux chamber deployment can be impossible and k estimates from tracer gas experiments can be biased (Asher and Wanninkhof 1998; Hall and Madinger 2018). Many of the alternative methods are also limited to bubble free low gradient systems, including turbulence measurements (Kokic et al. 2018), eddy covariance techniques (Huotari et al. 2013; Berg and Pace 2017), time series analysis of O₂ concentrations (Holtgrieve et al. 2010; Appling et al. 2018), and empirical equations that relate measured k to channel hydraulics (Bennett and Rathburn 1972; Melching and Flores 1999; Raymond et al. 2012). To overcome these limitations, fundamentally new approaches need to be explored to accurately estimate k in bubbly flow.

Turbulence and air bubbles emit excess energy as acoustics waves. The sound of turbulence, typically with frequencies of 20–100 Hz, is generated by eddies that do not contribute to dissipation of turbulent kinetic energy (TKE) (Proudman 1952; Lighthill 1954; Bassett et al. 2014). The sound of bubbles, typically with frequencies of 250–4000 Hz, is generated when air is entrained into a breaking water surface and starts to pulsate in volume under turbulent pressure fluctuations (Minnaert 1933; Leighton and Walton 1987). The sound of running water contains contributions from both turbulence and bubbles and therefore provides valuable information to estimate k.

Given the known linkages between k and turbulence/bubbles as well as turbulence/bubbles and sound signature, it should be possible to predict k based on sound. Sound spectral analysis has, to our knowledge, never been explored in attempts to estimate k. Above-stream sound pressure levels (SPLs) and k measured by propane injections experiments are highly correlated (R² = 0.94; Morse et al. 2007). Past SPL measurements (Morse et al. 2007) were done above the stream surface and integrated the whole audible frequency spectrum, making them sensitive to background noise. A more accurate and integrative approach could be to capture the sound underwater where it is produced and to target frequency bands directly associated to turbulence and bubbles. Such an approach may also hold potential to investigate unexplored relationships between the different mechanisms that contribute to underwater sound and k.

Here, we developed and tested a new method to estimate k based on the sound of running waters recorded above and below the water surface with calibrations against k derived from flux chamber measurements of CO₂ exchange. As a proof-of-concept, we first explored the relationship between k and sound spectral characteristics under controlled lab conditions. We then used lab insights to evaluate field observations in Swedish headwater streams. We assessed relationships between k and sound spectral properties separately for specific sites, across sites of similar surface flow types, and across all sites. We predicted strong relationships for sound signatures associated with bubbles and turbulence relative to background noise. We expected stronger relationships to result from site-specific relative to general comparisons, from sound measured underwater relative to above the water surface, and from surface flow types associated with high relative to low turbulence and bubble entrainment. We assessed the predictive power of acoustic indices relative to conventional hydraulic indices.

Materials and procedures

Overview

We combined a laboratory bubble plume experiment and field observations in streams to evaluate relationships between k and sound spectral properties across a wide range in artificial and natural gradients in turbulence and bubble entrainment. We established statistical k models based on indices of SPLs and, as a reference, on hydraulic characteristics. We first introduce the experimental design of the lab and field experiment and then describe measurement techniques: a gas flux chamber to measure k, microphones and hydrophones to measure sound above and below the water surface, and an acoustic Doppler velocity (ADV) meter to estimate turbulence. Unless otherwise specified, all statistical packages and data analyses were performed in R (R Development Core Team 2015).

Lab experiments

A bubble plume experiment was performed to generate a wide range of turbulence and bubble conditions in a controlled environment. The experiment was performed in a 0.1 m³ experimental chamber (Figs. 1, 2A–C) filled with tap water (19 ± 1°C) to levels of 15 and 25 cm to cover a depth range typical for headwater streams. To generate turbulence and bubbles, and hence stimulate k, we diffused nitrogen gas through a cylindrical air diffuser (10 cm length, 5 cm diameter, 100–200 μm pore size) centered at the bottom of the chamber. Nitrogen was injected at three replicate cycles, each consisting of 16 different set rates of gas flow (Q of 0, 0.002, 0.02, 0.045, 0.09, 0.22, 0.37, 0.5, 1, 2, 3, 4, 6, 10, 15, and 25 L min⁻¹). Q was regulated at a constant pressure of 2 bars by a gas regulator (RB 35/A BG, AGA gas AB, Lidingö, Sweden) and monitored by gas flow rotameters (EW-32457-42, Cole & Parmer, Vernon Hills, IL, U.S.A., for Q ≤ 1 L min⁻¹; ZYIA LZM-6T, Yuyao Kingtai Instrument, Zhejiang, China, for Q > 1 L min⁻¹). Q was converted to superficial gas velocities, U = Q/A, where A was the cross-sectional diffuser area (Schierholz et al. 2006). For each level of Q, triplicate measurements of stereo sound, k, three-dimensional water flow velocities and air- and water CO₂ concentrations were collected consecutively by methods described further below. Estimates of k were based on measurements of CO₂ evasion. Evasion resulted from supersaturation of CO₂ in the water (6000–8000 ppm) relative to the ambient air (500–600 ppm). To establish supersaturation, we exhaled CO₂-rich air through the diffuser prior to each set of nitrogen injection experiments until the above-mentioned target concentration was reached.

Figure 1

Photographs of bubble plumes in the experimental chamber with two hydrophones placed above an air diffuser with superficial gas velocities of 7 × 10⁻⁵ m s⁻¹ (A), 3 × 10⁻⁴ m s⁻¹ (B), 3 × 10⁻³ m s⁻¹ (C), and 3 × 10⁻² m s⁻¹ (D); and photographs of field sites of different surface flow types including smooth boundary turbulent (E), rippled (F), standing wave (G), and chute (H).

Figure 2

Experimental setup of the lab (A–C) and field (D–G) observations including air–water gas exchange velocity measurements by a flux chamber (A, D, gray shading in G), acoustic measurements by microphones (B, E) and hydrophones (C, F), and measurements of stream morphology and hydraulics (G).

The experimental chamber was enclosed by 30 mm thick foam wrapped in aluminized polyester film (Biltema 369,219, Biltema AB, Helsingborg, Sweden) and placed in a 3 mm thick plastic box (Fig. 2B, Supporting Information Fig. S1). The chamber walls were tilted to avoid formation of standing waves and wall edges were sealed watertight with silicone rubber. A removable foam top allowed access to the chamber and contained holes fitted for mountings, gas tubes, and cables. This design allowed a clear reduction in background noise originating from outside the chamber (−6 dB at 500 Hz). To further minimize background noise, the lab experiment was done outside office hours at the Department of Ecology and Environmental Science, Umeå University, Umeå, Sweden, and all potentially disturbing sound sources (air conditioning, appliances) were switched off during sound recording.

Field experiment

Field observations were conducted under a wide range of flow conditions in three headwater forest streams in boreal Sweden (Table 1). The streams were inlets to the lakes Övre Björntjärn, Struptjärn, and Lillsjölidtjärnen and hereafter referred to by the names of the lakes they enter. Bottom substrates differed within and between streams and were dominated by sand, gravel, cobbles, and boulders in Övre Björntjärn, organic material in Struptjärn, and sand, gravel, and organic material in Lillsjölidtjärnen. The regional hydrology is characterized by pronounced spring floods in April–May, summer and winter low flow periods, and autumn storms in September–November. For more details on the streams, see Klaus et al. (2018).

Table 1. Morphological and hydrological parameters of the studied streams.

Catchment	Latitude (°)	Longitude (°)	Catchment area (ha)	Reach length (km)	Whole stream length (km)	Mean depth (m)	Mean width (m)	Discharge range (L s^−1)	Reach slope (%)	Whole stream slope (%)
Lillsjölidtjärnen	63.844	18.620	19	0.21	0.6	0.3 ± 0.1	0.4 ± 0.1	0.9–12.9	3.4	4.0
Struptjärn	64.021	19.487	46	0.22	1.4	0.3 ± 0.1	0.6 ± 0.1	0.2–54.8	2.4	1.9
Övre Björntjärn	64.126	18.776	233	0.21	3.0	0.3 ± 0.1	0.8 ± 0.3	7.2–113.8	2.4	1.9

• Mean channel depth and width are given as means ± SD across sampling sites. Discharge, depth, and width relate to conditions during field sampling in May 2014–April 2015.

Stream reaches of around 200 m length were chosen that cover streambed morphology, surface flow, and bottom substrate types representative of the whole stream. Within each reach, 12 representative sites were selected. The sites were classified according to four different surface flow types (Padmore 1998) as observed in late May 2014: smooth boundary turbulent (SB), rippled (RI), standing wave (SW, including unbroken and broken waves), and chute (CH) (Fig. 1; Table 2). At each site, k and sound was determined using triplicate flux chamber and single stereo acoustic measurements as shown in Fig. 2E,F and described in detail below. In addition, channel slope, stream depth (d), stream width, flow velocity (V), and discharge were determined at each site within a 1.5 m long reach (Fig. 2G, Supporting Information Text S1). Froude numbers (Fr = V × [d × 9.81 m s⁻²]^−0.5) and Reynolds numbers (Re = Vdδν⁻¹) were computed where δ was water density following Chen and Millero (1986) and ν was the dynamic viscosity following Sengers and Watson (1986). Each study site was sampled four to eight times between May 2014 and April 2015 to cover a wide range of water temperature (0–17°C) and discharge (0.2–113.8 L s⁻¹, Table 2). The covered range in discharge corresponded to the 8^th–94^th, 1^st–97^th, and 17^th–85^th percentile of hourly discharge measurements during 01 April–31 October in 2012–2015 in Lillsjölidtjärnen, Struptjärn, and Övre Björntjärn, respectively (Klaus et al. 2018).

Table 2. Morphological and hydrological characteristics (means ± SD) of the field sampling sites for different surface flow types.

Flow type	Symbol	n	Depth (cm)	Width (cm)	Discharge (L s^−1)	V (m s^−1)	Fr	10^3 Re	Slope (m m^−1)	k600 (m d^−1)
Smooth boundary turbulent	SB	11	31 ± 14	75 ± 25	19 ± 12	0.17 ± 0.12	0.10 ± 0.08	36 ± 21	0.003 ± 0.003	2.1 ± 0.6
Rippled	RI	11	25 ± 12	48 ± 16	13 ± 11	0.20 ± 0.16	0.13 ± 0.10	36 ± 35	0.014 ± 0.020	3.3 ± 1.3
Standing wave	SW	8	20 ± 6	67 ± 35	20 ± 11	0.42 ± 0.24	0.29 ± 0.18	62 ± 38	0.066 ± 0.037	7.3 ± 4.5
Chute	CH	6	30 ± 12	59 ± 10	21 ± 11	0.68 ± 0.31	0.42 ± 0.24	126 ± 40	0.112 ± 0.044	19.0 ± 22.1

• Standard deviations reflect variability across sites. V, flow velocity; Fr, Froude number; Re, Reynolds number; k₆₀₀ = air–water gas exchange velocity.

Audio recordings

Aerial sound was acquired using omnidirectional digital audio recorders (DR-05, TASCAM, Montebello, CA, U.S.A.) with a nominal sensitivity of −125 dB re 1 V/μPa and a flat frequency response (+1/−3 dB) in the range of 20 Hz–20 KHz. Audio signals of at least 35 s length were sampled at a rate of 44.1 kHz with 24 bit resolution. The microphones were equipped with a 12 mm thick foam wind screen and mounted to a tripod facing downward. The sensors were located centered and 30 cm above the experimental chamber bottom in the laboratory and 30 cm above the stream water surface in the field experiment (Fig. 2B,C,E). Start and end points of recordings were marked by whistling loudly. Repeatability was high, indicated by average standard deviations (SDs) of ± 2.8 dB across triplicate recordings taken at randomly chosen sites on selected sampling occasions (max. ± 5.1 dB, n = 10).

Underwater sound was acquired using two calibrated omnidirectional low flow noise hydrophones (BII-7016, Benthowave Instrument, Collingwood, Ontario, Canada) with a nominal sensitivity of −198 dB re 1 V/μPa and a flat frequency response (± 2 dB) in the range of 0.1 Hz–60 KHz. The hydrophones were connected to a preamplifier with 26 dB flat gain and 30 Hz high-pass filter (BII-1006 T1, Benthowave Instrument). System self-noise was at least 6 dB below Knudsen's Sea State Zero (minimum ambient noise in the ice-free sea with no waves and a flat water surface; Knudsen et al. 1948) at frequencies of 1 Hz–1 KHz. Audio signals of at least 35 s length were sampled at a rate of 44.1 kHz with 24 bit resolution and stored on a portable digital audio recorder (DR-100mkII, TASCAM) with a nominal sensitivity of −171.5 dB re 1 V/μPa and a flat frequency response (+1 dB/−3 dB) in the range of 20 Hz–20 KHz.

For lab and field deployment, the hydrophones were mounted on a stainless steel structure fixed on a tripod designed to disturb the flow field as little as possible (Fig. 2C,F). In the lab experiment, the hydrophones were placed centered in the experimental chamber. For field measurements, the units were oriented parallel to the channel flow. Cables were laid inside the mounting to avoid vortex shedding in the water current. To minimize sound scatter, we presoaked the hydrophones before any recording. Presoaking ensured no air bubbles were trapped in the mounting or would form on the hydrophone surface due to boundary layer heating (Robinson et al. 2014). The hydrophone units were installed parallel with a free distance of 3 cm to each other and 3 cm to the water surface. This design allowed us to evaluate the risk of self-noise induced by water flow around the apparatus. Such self-noise was never an issue as indicated by very high spectra similarity (S) between the two hydrophones (Buck and Greene 1980, S = 0.98 ± 0.02 as a mean ± SD across all measurements, calculated using the “simspec” function of the R package “seewave”; Sueur et al. 2008).

Within-site variation in underwater SPLs, according to data taken 30 cm upstream and downstream of each measuring site, was low (± 2.6 dB as a mean over all octave bands, max. ± 7.5 dB, n = 201). Repeatability was high, indicated by average SD of ± 0.9 dB across triplicate recordings taken at randomly chosen sites on selected sampling occasions (max. ± 3.7 dB, n = 12).

The microphones and hydrophones were intercalibrated three times during the study period in a characterization chamber placed in an anechoic room of the Division of Speech-Language Pathology, Institute of Clinical Science, Umeå University. Intercalibrations showed no systematic difference across left and right channels and over time (Supporting Information Text S2).

As our lab experiment was not designed to fully disentangle turbulence from bubble effects on sound spectra, we also investigated the sensitivity of our hydrophones to turbulence alone. To do so, we performed additional comparative hydrophone and ADV measurements in a stream on the campus of Umeå University in October 2018. Here, we investigated correlations between SPLs at frequencies associated with turbulence and turbulence derived from ADV reference measurements (for details, see Supporting Information Text S4).

Gas flux chamber measurements

Air–water gas exchange velocities were measured using a static gas flux chamber following the protocol by Klaus et al. (2018) unless declared elsewise below. Briefly, the chamber had an elongated hexagonal cross-section with rounded edges to minimize flow disturbance, mounted to a tripod and placed on the water surface with its side walls extending 2 cm into the water. The flux chamber was placed in the middle of the lab experimental chamber or centered in the stream with the main axis oriented in flow direction (Fig. 2A,D). Gas exchange measurements consisted of triplicate cycles of CO₂ accumulation and aeration phases each 4–8 and 1–2 min long. In the lab experiment, CO₂ concentrations in the chamber were measured every 10 s using an infrared gas analyzer (EMG-4, PP-Systems, Amesbury, MA, U.S.A.), calibrated against reference gas mixtures with CO₂ concentrations of 800, 3000, and 8000 ppm (AGA gas AB). During field experiments, CO₂ concentrations in the chamber were measured using a nondispersive infrared CO₂ sensor (CO2 Engine® ELG, SenseAir AB, Delsbo, Sweden) that was calibration-checked against N₂ gas before each field visit (Bastviken et al. 2015). Gas exchange measurements yielded three linear regression slopes that described the rise in CO₂ concentration in the chamber over time. The gas exchange coefficient k was calculated using Fick's law of diffusion k = F(d (c_wat − c_eq))⁻¹, where F is the CO₂ flux as estimated by the linear regression slopes, c_wat is the arithmetic mean CO₂ concentration in water measured at the beginning and the end of the flux chamber deployment period, and c_eq is the CO₂ concentration of water if it was in equilibrium with ambient air calculated from measured air concentration and water temperature using Henry's constant. Here, chemical enhancement of CO₂ flux by hydration reactions of CO₂ in water was assumed to be negligible because pH was always well below 8 (Wanninkhof and Knox 1996). Partial pressure of CO₂ in the water was measured by a handheld nondispersive infrared CO₂ sensor (CARBOCAP GM70, Vaisala, Helsinki, Finland) with a sensor probe (CARBOCAP GMP220) enclosed in a semipermeable polytetrafluoroethylene membrane, following the methods established by Johnson et al. (2010). The CO₂ sensor was calibrated against reference gas mixtures with CO₂ concentrations of 800, 3000, and 8000 ppm (AGA gas AB) where linear regressions between the probes voltage signal and known concentrations had R² > 0.99.

Molar CO₂ concentrations were derived from Bunsen solubility coefficients using water temperature-parameterizations in Weiss (1974). In situ water temperature specific k values were normalized to 20°C to yield k₆₀₀ values following Jähne et al. (1987) using Schmidt number parameterizations for freshwater and water temperature according to Wanninkhof (1992). Water temperature was measured using a digital thermometer (Ama-digit ad 15^th, Amarell GmbH & Co. KG, Kreuzwertheim, Germany). Reported errors in k₆₀₀ values were the propagated standard errors (SEs) of regression slopes of CO₂ concentration increases over time.

Flux chamber k₆₀₀ estimates were compared to independently measured k₆₀₀ values using a propane gas injection technique, available for four subreaches per stream, where k estimated from propane loss downstream was converted to k₆₀₀ for standardized comparison among gases (Jähne et al. 1987). The arithmetic mean k₆₀₀ across three flux chambers located in each subreach correlated strongly with subreach specific k₆₀₀ values from propane-injection experiments, but underestimated subreach specific k₆₀₀ by 39% (linear regression, slope = 0.61, p < 0.001, R² = 0.58, n = 42, Klaus et al. 2018). Flux chamber k₆₀₀ estimates were also assessed on potential bias by chamber-induced turbulence (Lorke et al. 2015) by comparative ADV measurements with and without the chamber placed in a stream on the campus of Umeå University in October 2018 (Supporting Information Text S4).

TKE estimation

In the laboratory experiment, we estimated TKE of the bubble plume from three-dimensional flow velocity measurements using an ADV (Argonaut-ADV®, SonTek/Xylem, San Diego, CA, U.S.A.). We sampled a water volume of 0.25 cm³ at a distance of 10 cm from the transducer for 1 min at 25 Hz using a down-looking 10 MHz probe, with an upper velocity limit set to 3–30 cm s⁻¹. To avoid interference with the main flow direction in the bubble plume, we oriented the probe at an angle of 40° to the main axis of the diffuser stone (Fig. S1). We sampled two water volumes at a depth of 7 cm below the water surface: one centered inside and one outside the bubble plume. The location outside the bubble plume was the location closest to the gas stone that was unaffected by bubbles when choosing the highest nitrogen gas flow. Bubble-induced amplitude spikes in flow velocities were removed following Birjandi and Bibeau (2011) to avoid overestimation of TKE (Supporting Information Text S3). TKE was then calculated as , where sv _x, sv _y, and sv _z are the SDs of flow velocities in x, y, and z direction, respectively. TKE was expressed as the geometric mean of estimates inside and outside the bubble plume.

Audio signal processing

Audio records were converted from the time to the frequency domain using short-term Fourier transform and expressed as mean SPLs for 11 octave bands from 16 Hz to 16 kHz using the “meanspec” function of the R package “seewave.” Here, audio records were segmented using Hanning windows of 16,384 data points (≈ 0.37 s), an overlap between two successive analysis windows of 50% and standard dB reference values of 1 μPa for water and 20 μPa for air. To avoid potential disturbance from handling the recorder, the first and last 2–3 s of audio records were excluded. Prior to further processing, spectrograms and oscillograms of each recording were carefully inspected visually. About 5% of these recordings contained pronounced spikes, presumably caused by collisions of objects such as leaves or branches with the hydrophone, and excluded from further processing by selecting shorter record sections free from spikes.

To summarize the spectral data, the mean and SD of the SPL was computed for each octave band using the “meandB” and “sddB” functions of the R package “seewave.” Octave-specific statistics were then averaged across the left and the right microphone or hydrophone channels, justified by their high spectra similarity (S = 0.98 ± 0.02 and S = 0.95 ± 0.0, respectively). Differential SPLs (dSPLs) were calculated as the difference in SPL between a signal and background octave affected and unaffected by turbulence or bubbles. This approach allowed for intercomparison among recordings even though recording devices were not calibrated to reference sound level meters and hence did not yield absolute SPLs. A number of plausible signal and background octaves were selected based on observations in the lab experiments.

Linking sound spectra to k₆₀₀

The laboratory experiment was used to gain insights in shifts in sound spectra depending on turbulence and bubble conditions. Data were explored using a series of biplots of k₆₀₀, TKE, k₆₀₀/TKE (as a proxy of the efficiency of gas exchange at a given level of TKE), and dSPLs of characteristic signal octaves associated with turbulence and bubbles against superficial gas velocities, U. Similarly, we explored field data using biplots of site-specific mean k₆₀₀ and dSPLs against channel slope (as a proxy of bubble entrainment) and individual observations of k₆₀₀ and dSPLs against Fr numbers (as a proxy of turbulence).

Relationships between k₆₀₀ and dSPLs were quantified using univariate linear regression analysis. Laboratory relationships were modeled separately for each water depth using the “lm” function in R. For field data, relationships were tested separately for each surface flow type, and generally across all sites using linear mixed-effect (LME) models. Here, the factor “site” nested in “stream” was included as a random effect on the intercept. Accounting for site-specific rather than general intercept terms yielded significantly better model fits (lower Akaike's information criterion values) according to the likelihood ratio test carried out by means of the R “anova” function. We fitted LME models using the restricted maximum likelihood algorithm of the “lme” function of the R package “nlme” (Pinheiro et al. 2018). All models were evaluated based on the marginal and conditional coefficient of determination (R²_m, R² _c; i.e., the variance in the dependent variable explained by the fixed effect, and fixed and random effects, respectively), the p value of the fixed effect, and the root mean squared prediction error based on leave-one-out 10-fold cross-validation (CV-RMSPE) where the 10% largest differences between measured and observed values were trimmed. We calculated R² _m and R² _c using the “r.squaredGLMM” function of the R package “MuMIn” (Barton 2018). The CV-RMSPE was calculated using the “cvFit” function of the R package “cvTools” (Alfons 2012).

For field data, we also investigated the potential of site-specific variability in proxy performance. For each site, we fitted a number of candidate linear regression models using the “lm” function in R, each based on dSPLs with different signal octaves and, as a reference, different hydraulic parameters (Fe, Re, V, discharge, depth:width ratio). The signal octave and hydraulic parameter that maximized the explained variance in k₆₀₀ was chosen for the final acoustic and hydraulic site-specific models, respectively. We tested whether linear model performance (R², p value of model slope, CV-RMSPE) differed between indices (microphone vs. hydrophone, and hydrophone vs. hydraulics based models), among surface flow types (SB and RI vs. SW and CH) and their interaction, using two-way ANOVA (“aov” function in R). We investigated the nature of significant interactions by testing on differences in model performance between indices within SB and RI, and within SW and CH, respectively, using two-sample t-tests (“t.test” function in R). We log-transformed CV-RMSPE and p values of model slopes to conform assumptions of normality in ANOVAs and t-tests.

Spectral shift assessment

To challenge our static approach of using fixed signal bands, we also assessed the temporal variability in key sound spectral properties. We generated four time waves of lab and field microphone and hydrophone recordings, each including six 10 s sequences recorded at different k₆₀₀ levels. To visualize spectral dynamics over time, a two-dimensional spectrographic representation of a time wave was generated using the “spectro” function of the R package “seewave” with the same settings as for the “meanspec” function described above. To further investigate potential frequency shifts in signal octaves, peak frequencies (i.e., the octave bands associated with the maximum SPL) were extracted from all audio records and plotted against k₆₀₀.

Assessment

Laboratory experiment

Sound spectral properties of the bubble plume shifted as U changed from 0 to 0.08 m s⁻¹ (Fig. 3). In general, SPLs decreased from low to high frequencies as long as U was relatively low. However, with progressively higher U, an SPL peak with a spectral prominence of up to 50 dB formed at 250–4000 Hz, indicating increased bubble contributions (Minnaert 1933; Leighton and Walton 1987). This peak declined sharply under the water surface (Fig. 3C,D) but leveled off smoothly toward higher frequencies above the water surface (Fig. 3A,B) because high-frequency sound is attenuated more strongly in water than in air. Under the water surface, SPLs increased with U even at frequencies around 31.5 Hz, indicating an increase in turbulence (Proudman 1952; Lighthill 1954; Bassett et al. 2014) that was not detectable in air. Based on the laboratory insights described above, we chose SPL at 31.5 Hz (SPL_31.5) as a proxy of turbulence (for underwater sound), SPL at 1 kHz (SPL₁₀₀₀) as a proxy of bubbles (for air and water sound), and the arithmetic mean SPL across all bands that showed marked shifts with U (250–4000 Hz in air, and 31.5–1000 Hz in water) as indices of k₆₀₀ (Table 3). SPLs at 31.5 Hz (air) and 16 kHz (water) were relatively constant and therefore subtracted as background noise from signals to yield SPL_250–4000-SPL_31.5 and SPL_31.5–1000-SPL₁₆₀₀₀.

Figure 3

Sound pressure level spectra across 11 octave bands for 16 superficial gas velocities (U) recorded by microphones (A, B) and hydrophones (C, D) in the laboratory experimental chamber at water depths of 25 cm (A, C) and 15 cm (B, D). Shadings mark the octave bands associated with turbulence and/or bubbles (light gray) and background noise (dark gray).

Table 3. Signal and background octaves used for calculations of dSPLs as indicators of turbulence, bubbles, and air–water gas exchange velocities.

Medium	Process	dSPL symbol	Characteristic signal octave [Hz]	Alternative signal octaves [Hz]	Background octave [Hz]
Air	Turbulence	ND	ND	ND	ND
	Air bubbles	SPL1000-SPL31.5	1000	250, 500, 2000, 4000	31.5
	Air–water gas exchange velocity	SPL250–4000-SPL31.5	250–4000	—	31.5
Water	Turbulence	SPL31.5-SPL16000	31.5	63, 125	16,000
	Air bubbles	SPL1000-SPL16000	1000	250, 500	16,000
	Air–water gas exchange velocity	SPL31.5–1000-SPL16000	31.5–1000	—	16,000

• In air, turbulence was not detectable (ND).

To validate these hypotheses, trajectories of hydrodynamic and acoustic properties along gradients in U were assessed (Fig. 4). Accordingly, k₆₀₀ increased from 0.3 to 90 m d⁻¹ at rates similar to model predictions by Schierholz et al. (2006) as a result of interfacial and bubble-mediated gas exchange. TKE increased from 3 × 10⁻⁵ to 2 × 10⁻³ m² s⁻², but only after U exceeded 0.001 m s⁻¹ (Fig. 4B). This increase was likely driven by plume-induced convection, collective oscillations of bubbles and bubble-amplification of turbulence (cf. Deane 1997; Wain and Rehmann 2005). The index k₆₀₀/TKE increased for U < 0.001 m s⁻¹, indicating that gas exchange became increasingly more efficient relative to available TKE as a result of increased bubble-mediated gas exchange (Fig. 4C). However, k₆₀₀/TKE reached a plateau for U ≥ 0.001 m s⁻¹, indicating that bubble volumes became so high that gas diffusion into bubbles became less efficient (Woolf et al. 2007). For U ≥ 0.03 m s⁻¹, k₆₀₀/TKE even started to decrease, likely because bubbles began to coalesce which decreased their surface area relative to their volume and hence the efficiency of gas exchange (Besagni et al. 2018). In this regime, the surface layer at the air–water interface became infinitely small so that the main resistance to gas exchange was at the air–water interface itself and became independent of turbulence (Noyes et al. 1996). As a result, k₆₀₀ leveled off at 90 m d⁻¹.

Figure 4

Hydrodynamic and acoustic indices as a function of superficial gas velocity (U) in the laboratory bubble plume experiment for different water depths. Hydrodynamic indices include: air–water gas exchange velocity (k₆₀₀) (A), TKE (B), and air–water gas exchange efficiency relative to turbulence (k₆₀₀/TKE) (C). Acoustic indices relate to microphone (D–F) and hydrophone recordings (G–I) and refer to SPLs averaged across octave bands associated with turbulence and/or bubbles (D, G) and at single octave bands associated with turbulence (E, H) and bubbles (F, I). Lines in panel (A) show predictions by Schierholz et al. (2006).

The shifts in turbulence and bubble contributions to k₆₀₀ were strongly reflected in the sound spectra. Under water, dSPLs associated with turbulence largely followed trends in TKE, increasing by 20 dB for U ≥ 0.001 m s⁻¹ (Fig. 4H). Above the water surface, SPL_31.5 remained unaffected by turbulence (Fig. 4E). Both above and under water, dSPLs associated with bubbles largely followed k₆₀₀/TKE with main increases of 50 dB for U < 0.001 m s⁻¹ and decreases for U > 0.03 m s⁻¹ (Fig. 4F,I). As a result, aerial and underwater sound pressure levels averaged across octave bands associated with bubbles (SPL_250–4000-SPL_31.5) and turbulence and bubbles (SPL_31.5–1000-SPL₁₆₀₀₀) increased steadily with U (Fig. 4D,G) and provided excellent indices of k₆₀₀ with parameterizations independent of water depth (Fig. 5; Table 4). Mean (±SD) parameterizations across both depths were:

(1)

(2)

Figure 5

Air–water gas exchange velocity (k₆₀₀) as a function of SPLs measured with microphones (A) and hydrophones (B) in a laboratory bubble plume with water depths of 15 and 25 cm. The solid lines show linear regression fits. Error bars show propagated SEs of triplicate measurements. The circle marks an outlier excluded from the regression. For regression model details, see Table 4.

Table 4. Statistical details of the linear regression models explaining air–water gas exchange velocity (k₆₀₀) by aerial sound pressure levels (SPL_250–4000-SPL_31.5), under water sound pressure levels (SPL_31.5–1000-SPL₁₆₀₀₀) and Froude number (Fr) as shown in Figs. 5, 7F, 8.

Scale	Figure	Proxy	Water depth (m) / surface flow type	Slope				Intercept				CV-RMSPE	R^2 m	R^2 c	df
				Mean	Std.	t	p	Mean	Std.	t	p
Lab	5A	SPL250–4000-SPL31.5	0.15	0.25	0.02	15.5	0.00	9.51	0.51	18.5	0.00	0.45	0.95	NA	14
			0.25	0.26	0.02	16.7	0.00	9.70	0.48	20.2	0.00	0.41	0.95	NA	14
	5B	SPL31.5–1000-SPL16000	0.15	0.25	0.02	13.3	0.00	−7.54	0.71	−10.7	0.00	0.48	0.93	NA	14
			0.25*	0.25	0.01	46.2	0.00	−7.19	0.20	−36.2	0.00	0.17	0.99	NA	13
Field	8A	SPL250–4000-SPL31.5	SB	0.06	0.02	3.09	0.00	1.30	0.38	3.45	0.00	0.90	0.14	0.14	48
			RI	0.01	0.02	0.28	0.78	0.79	0.50	1.57	0.13	1.11	0.00	0.09	40
			SW	0.08	0.01	5.72	0.00	1.76	0.22	7.97	0.00	0.90	0.43	0.50	37
			CH	0.09	0.02	4.57	0.00	1.59	0.50	3.21	0.00	0.94	0.42	0.66	27
			All	0.07	0.01	9.01	0.00	1.68	0.15	11.43	0.00	0.97	0.36	0.45	155
	8B	SPL31.5–1000-SPL16000	SB	0.10	0.05	2.01	0.05	−0.27	0.28	−0.98	0.33	0.92	0.06	0.06	48
			RI	0.07	0.03	2.04	0.05	0.21	0.29	0.72	0.47	1.03	0.07	0.21	40
			SW	0.09	0.01	8.72	0.00	−0.17	0.39	−0.43	0.67	0.69	0.50	0.71	41
			CH	0.11	0.01	11.3	0.00	−0.40	0.62	−0.64	0.53	0.57	0.53	0.86	34
			All	0.09	0.01	12.6	0.00	−0.15	0.27	−0.57	0.57	0.84	0.46	0.59	166
	7F	Fr	SB	4.31	0.83	5.21	0.00	−0.13	0.15	−0.86	0.39	0.79	0.34	0.34	42
			RI	4.07	0.86	4.75	0.00	0.11	0.22	0.50	0.62	0.88	0.35	0.37	34
			SW	2.53	0.42	6.02	0.00	0.53	0.36	1.49	0.14	0.83	0.39	0.51	39
			CH	1.41	0.43	3.26	0.00	1.27	0.71	1.80	0.08	1.08	0.14	0.61	31
			All	2.68	0.26	10.4	0.00	0.35	0.23	1.51	0.13	0.90	0.37	0.47	149

• * One outlier removed with Cook's distance of 0.5.
• Std., standard deviation, CV-RMSPE, cross-validated root mean square prediction error; R² _m, marginal coefficient of determination (variance proportion explained by fixed effects; conventional R² for lab data); R² _c, conditional coefficient of determination (variance proportion explained by fixed and random effects); SB, smooth boundary turbulent; RI, rippled; SW, standing wave; CH, chute.

Field experiment

The streams had widely different morphological and hydrological characteristics with increasing flow velocities, slopes, and k₆₀₀ from SB to RI, SW, and CH surface flow types (Table 2). Accordingly, sound spectra shifted dramatically (Fig. 6). In SB and RI, SPLs decreased from low to high frequencies. However, toward more turbulent surface flows (SW, CH), an SPL peak formed at around 500–1000 Hz, indicating increased bubble contributions. Under the water surface, SPLs increased even at frequencies around 31.5 Hz. Overall, spectral shapes closely resembled lab observations (cf. Fig. 3).

Figure 6

Sound pressure level spectra across 11 octave bands of microphone (A) and hydrophone (B) recordings in natural streams. Circles and error bars show geometric means ± SD across different surface flow types. Shadings mark the octave bands associated with turbulence and/or bubbles (light gray) and background noise (dark gray). Symbols are jittered along the frequency axis to reduce overlap.

Estimates of k₆₀₀ and acoustic indices varied in concert with key morphological and hydraulic variables (Fig. 7). Both site-specific mean k₆₀₀ and SPL₁₀₀₀ relative to background noise increased with channel slope (Fig. 7A,C,E), indicating increased bubble contributions to sound and gas exchange (cf. Cirpka et al. 1993; Hall and Madinger 2018). Under water, SPL_31.5-SPL₁₆₀₀₀ increased with channel slope (Fig. 7D), indicating enhanced turbulence at steeper sites. Increases in k₆₀₀ with Fr were reflected in parallel increases in SPL₁₀₀₀ relative to background noise both above and under water, and in SPL_31.5-SPL₁₆₀₀₀ under water (Fig. 7F,H–J). The increase of SPL_31.5-SPL₁₆₀₀₀ with Fr persisted even for conditions where SPL₁₀₀₀-SPL_31.5 < 5 dB re 1 μPa, i.e., in the absence of bubbles (Supporting Information Fig. S7). Above the water surface, SPL_31.5 did not increase with channel slope or Fr (Fig. 7B,G). Overall, field data confirm that k₆₀₀ and SPLs were driven by the same hydraulic processes. As a result, dSPLs predicted k₆₀₀ reasonably well (Fig. 8, Table 4). The general relationships across all sites (means±SD) were described by

(3)

(4)

Figure 7

Air–water gas exchange velocity (k₆₀₀) and acoustic indices as a function of channel slope (A–E) and Froude number (Fr, F–J) in natural streams with different surface flow types. Symbols and error bars refer to means ± SD across different sampling occasions (A–E) or triplicate measurements (F–J). Vertical lines in (F–J) mark Fr = 0.05, here corresponding to Re of around 12,500 and hence the onset of turbulent flow, and Fr = 1, corresponding to the onset of supercritical flow.

Figure 8

Air–water gas exchange velocity (k₆₀₀) as a function of SPLs measured with microphones (A) and hydrophones (B) in natural streams with different surface flow types. Symbols and error bars show propagated means ± SD across triplicate measurements. The solid lines show linear regression fits and follow the same color coding as the circles. For regression model details, see Table 4.

The dSPL indices explained 36% and 46% of the within-site variance in k₆₀₀ with prediction errors of ± 0.97 and ± 0.84 m d⁻¹. Hydraulic indices performed equally (37% and ± 0.90 m d⁻¹ for Fr, Table 4, for other hydraulic indices, see Supporting Information Table S3). Relative to general models, surface flow type specific models had higher R² _m (0.42–0.53) and lower CV-RMSPE (± 0.57–0.94 m d⁻¹). Model slopes and intercepts were similar across surface flow types (Fig. 8), but model performances differed (Table 4). Importantly, acoustic indices performed better than hydraulic indices in bubbly flow (SW, CH), while the opposite was true in non-bubbly flow (SB, RI) (Table 4, Supporting Information Table S3). For example, relative to Fr-based models, the hydrophone-based dSPL index yielded higher R² _m (0.50–0.53 vs. 0.14–0.39) and lower CV-RMSPE (0.57–0.69 vs. 0.83–1.08 m d⁻¹) in SW and CH.

Relative to flow type-specific models, site-specific models explained a higher proportion of variance in k₆₀₀ (R² = 50–90%, Fig. 9). Hydrophone-based models performed generally better than microphone-based models with higher R² (two-way ANOVA [here and hereafter, if not declared elsewise], F = 12.5, p < 0.001), lower p values of model slopes (F = 23.6, p < 0.001) and generally lower CV-RMSPE (F = 4.6, p = 0.03). There was no difference in R² and CV-RMSPE among surface flow types (F = 1.8, p = 0.19 and F = 1.4, p = 0.23), and differences between hydrophone- and microphone-based models did not differ between surface flow types (F = 0.4, p = 0.51 and F = 1.5, p = 0.22). Yet, p values differed among surface flow types (F = 14.1, p < 0.001) and these differences differed between hydrophone- and microphone-based models (F = 4.1, p = 0.046), being significant at a 1% level for SB and RI (two-sample t-test, t = −2.59), but at a 0.01% level for SW and CH (two-sample t-test, t = −4.48). Hydrophone- and hydraulics-based models generally performed equally well with similar R² values (F = 0.3, p = 0.57), p values of model slopes (F = 0.6, p = 0.44) and CV-RMSPE (F = 0.1, p = 0.74). There were no differences among surface flow types in R² (F = 0.2, p = 0.70) and CV-RMSPE (F = 0.0, p = 0.96) but in p values of model slopes (F = 8.3, p < 0.01). Differences in the performance between hydrophone- and hydraulics-based models showed a tendency for variation among surface flow types (F = 4.3, p = 0.04 for R²; F = 3.6, p = 0.06 for p values; and F = 2.6, p = 0.11 for RMSPE). Specifically, hydrophone- and hydraulics-based models performed equally well in SB and RI (two-sample t-tests, t = 1.6, p = 0.12 for R²; t = −0.6, p = 0.58 for p values; and F = −0.6, p = 0.52 for CV-RMSPE), but hydrophone-based models tended to perform better in SW and CH (t = −1.6, p = 0.13 for R²; t = 1.99, p = 0.06 for p values; and t = 2.2, p = 0.04 for CV-RMSPE).

Figure 9

Statistical performance of site-specific linear regression models relating air–water gas exchange velocities (k₆₀₀) to acoustical indices based on recordings by microphone (Mic) or hydrophone (Hyd) or to hydraulic indices (Mor). The boxplots summarize the distribution of the statistics of the candidate models with the highest coefficient of determination (R²) across all sites for each surface flow type, expressed by the median (thick solid line), interquartile range (box), first and third quartiles ± 1.5 times the interquartile range (whiskers), and remaining outliers (circles). Performance measures include the R² of linear regressions (A), the p value of the slope of linear regression models (B), and the CV-RMSPE (C). For comparison, performance measures of general models for cross-site comparisons are shown by triangles (cf. Table 4). As a reference, p values of 0.05 (B) and median k₆₀₀ across all measurements (C) are shown by dotted lines.

Spectral shifts

Given that the fit of site-specific models improved when the octave band selection for dSPL calculations was kept variable suggests that signal octave bands as indicators of k₆₀₀ may differ between stream sites but also that they may shift with changing flow conditions. To delve deeper into the spectral dynamics of recorded sounds through time, we provide four exemplary audio records and corresponding spectrograms (Fig. 10, Supporting Information Sound S1–S4). Each record consists of six 10 s long sequences of above- and under-water sound, recorded under different flow conditions to span a wide range in k₆₀₀. Sound spectra shifted dramatically and similarly in the lab and in the field with increasing k₆₀₀. An SPL peak became progressively more pronounced, wider and shifted toward lower frequencies from 2000 to 500 Hz. This shift indicates an increasing bubble volume, collective bubble oscillations, and/or an increase in the dominant air bubble size (Minnaert 1933;Yoon et al. 1991 ; Loewen and Melville 1994). Oscillating motions associated with bubbles or turbulence were apparent from second-scale fluctuations in SPLs (Fig. 10). Shifts in SPL peak frequencies with increasing k₆₀₀ were a general phenomenon in underwater but not above water sound (Fig. 11). Under water, peak frequencies were most often ≤ 250 Hz in SB and RI with k₆₀₀ < 10 m d⁻¹. These peaks were associated with turbulence and indicate limited bubble contributions. Yet, at SW and CH, midfrequency peaks gained dominance and shifted from 4000 to 500 Hz with a 1–2 magnitude increase in k₆₀₀. Above the water surface, peaks clustered either at ≤ 250 Hz or around 1000 Hz, independent of lab or field conditions. As a result, there is no single fixed octave band that correlates with shifts in k₆₀₀, but instead the location of the signal band in the frequency spectrum is dynamic and reflects frequency shifts in signals of processes associated with air–water gas exchange.

Figure 10

Spectrograms of SPLs recorded by microphones (A, C) and hydrophones (B, D) in the laboratory bubble plume experiment (A, B) and in a natural stream (C, D). The spectrograms consist of six 10 s sequences recorded at different superficial gas velocities in the laboratory at a water depth of 25 cm and during different field sampling occasions, respectively. Above each sequence, associated air–water gas exchange velocities (k₆₀₀) are shown. Audio records are available as wave files in the Supporting Information (Supporting Information Sound S1–S4). Note that SPLs are not calibrated to absolute values and should only be interpreted in terms of relative within-sequence differences.

Figure 11

Frequency of the octave band that yielded the maximum SPL as a function of air–water gas exchange velocity (k₆₀₀) for recordings by microphones (A) and hydrophones (B). Conditions included natural stream sites with different surface flow types (circles) and the laboratory experiment at different water depths (triangles).

Discussion

Passive acoustic techniques are increasingly used to survey aquatic ecosystems, yet their potential to monitor biogeochemical or ecological processes remain largely unexplored (Linke et al. 2018). Here, we demonstrate through lab and field observations that shifts in the contribution of bubbles and turbulence to sound and k₆₀₀ coincide, and that sound spectral analysis can be used to estimate k₆₀₀ in running waters. Compared to conventional methods, acoustic measurements are associated with reduced costs and sampling efforts. Efforts to calibrate acoustical instruments are minimized in our approach because we utilize cross-band differences and not absolute SPLs. These benefits make acoustic techniques unique in their potential to enhance the spatial and temporal resolution of k₆₀₀ estimates in turbulent running waters, and to provide a tool urgently needed to constrain the role of mountain streams in global estimates of gas fluxes (Ulseth et al. 2019). We also show the potential to use sound as an indicator of the different sources of k₆₀₀, enabling an improved mechanistic understanding of recently recognized distinct regimes in air–water gas exchange (Ulseth et al. 2019).

Our acoustic approach builds on pioneering work by Morse et al. (2007) that used above-stream SPLs, integrated over the whole audible sound spectrum, to predict k₆₀₀ and hydraulic parameters. Morse et al. (2007) were able to predict 94% of variability in single measurements of k₆₀₀ across 11 arctic headwater streams and 47–97% of variability in repeated measurements of stage height within six temperate forest streams. Our models performed slightly poorer (Fig. 9), likely because they spanned a discharge range that was an order of magnitude smaller. While a direct comparison of the performance of our approach and the approach by Morse et al. (2007) is not possible, it is intriguing that our approach yields nearly the same performance across a much narrower range of conditions. A clear strength of our approach is its flexibility in targeting octave bands to increase signals and avoid background noise. Underwater sound measurements may be an important way forward to improve k₆₀₀ predictions and provide mechanistic insights in the sources of k₆₀₀.

Our laboratory experiment provided insights in the acoustics of the drivers of gas exchange and assisted interpretations of field data. The laboratory experiment demonstrated that bubbles and turbulence caused characteristic sound patterns. The experiment was not primarily designed to distinguish between the single effects of bubbles and turbulence on sound spectra. However, bubble sound interfered likely only little, if at all, with turbulence sound, because the collective oscillation of bubbles in our plume can be expected to resonate at frequencies > 100 Hz and hence leaving SPL_31.5 largely unaffected (Yoon et al. 1991; Loewen and Melville 1994). This was confirmed by our field observations showing characteristic sound patterns in relation to turbulence proxies even in the absence of bubbles (Supporting Information Fig. S7). Further evidence was provided by additional comparative ADV and hydrophone measurements (Supporting Information Text S4). Here, SPLs at 16 Hz relative to background noise at 16 kHz increased clearly with TKE (Pearson correlation coefficient r = 0.77, n = 6, Supporting Information Table S2). However, given that the increase was less clear for SPL_31.5-SPL₁₆₀₀₀ (r = 0.06), we suggest future studies may use hydrophones with a broader frequency range to further explore the lower end of the frequency spectrum (< 20 Hz) as an indicator of turbulence.

The lab experiment was designed to give a first proof-of-concept of the acoustics of air–water gas exchange. For example, the experimental chamber lacked advective flow found in streams. While our lab experiment did not perfectly mimic field conditions (a common challenge in air–water gas exchange studies; Jähne et al. 1984), dSPL-k₆₀₀ relationships were qualitatively similar in our lab and field experiments (Figs. 5, 8). Differences in dSPL-k₆₀₀ relationships could be due to additional background noise in the laboratory in the low frequency domain (< 250 Hz). This noise resulted in a shift in SPL_31.5-SPL₁₆₀₀₀ by about 20 dB and could explain the difference in k₆₀₀ intercepts of about 7 m d⁻¹. What caused the differences in slopes is unknown, but could be related to the fact that water was standing in the laboratory but flowing in the field. Despite these lab-specific limitations, our field observations revealed k₆₀₀-dSPL relationships that were strikingly similar among surface flow types (Fig. 8) which corroborates the wide applicability of our field data derived dSPL model.

Our dSPL models explained a similar proportion of variation in k₆₀₀ as hydraulic parameters or published models based on stream morphological or hydrological characteristics (Bennett and Rathburn 1972; Melching and Flores 1999; Wallin et al. 2011; Raymond et al. 2012). Importantly, in bubbly flow (SW, CH), our acoustic indicators tended to perform better than hydraulic models, because they are a more direct indicator of bubble entrainment. Hydraulic parameters such as Fr can be high despite of an absence of air bubbles (Supporting Information Fig. S7).

Our calibration models estimated k₆₀₀ with prediction errors of ± 0.6–1 m d⁻¹, corresponding to 0.1–0.5 times the median k₆₀₀ (Fig. 9), indicating that the acoustic method is clearly superior relative to assuming a surface flow type specific mean k₆₀₀. Prediction errors were 1.5–2.5 times the analytical error of the flux chamber technique (mean SD across triplicates = ± 0.4 m d⁻¹). While gas flux chamber measurements took 5–10 min per replicate, acoustic measurements took only 0.5 min, and potentially less time is needed, given that signals were relatively stable even at 10 s scales (Fig. 10). This suggests a clear trade-off between accuracy and logistical efforts between methods and makes the acoustic method superior in scenarios with time-constrained field measurements.

Relative to general calibration models, surface flow type or site-specific models could in the best cases (hydrophone measurements in CH) explain double the variance and cut prediction errors in k₆₀₀ by half. Such system-specific calibrations allow for variable contributions of turbulence and bubbles to sound spectral signatures and k₆₀₀ depending on bubble size distributions and densities (Minnaert 1933; Yoon et al. 1991; Loewen and Melville 1994) but also for variations in propagation properties of sound depending on channel geometry and bottom structure (Forrest et al. 1993; Amoser and Ladich 2010; Tonolla et al. 2010). Surface flow-type or site-specific characteristics should be accounted for by initial calibration efforts in attempts to improve k₆₀₀ predictions.

Part of the remaining scatter in the dSPL-k₆₀₀ relationships could be explained by mismatches in the spatial integration of the methods. In contrast to flux chambers, the spatial integration of acoustic measurements is not well defined because sound waves are modified between source and receiver. In shallow water, hydrophones capture sound from within decimeters, because sound below around 1 kHz attenuates quickly with distance (Forrest et al. 1993; Lugli and Fine 2003; Tonolla et al. 2009). This makes the spatial integration of hydrophones comparable to that of the flux chamber technique. However, microphones capture sound from a larger area, because low-frequent sound propagates more efficiently in air. This scale-mismatch together with the lower affinity of microphones to turbulence-related noise and a higher affinity to background noise such as wind, animals, or infrastructure may explain the poorer performance of k₆₀₀ models based on microphones relative to hydrophones.

The validity of the provided acoustic-based k₆₀₀ models depends on the accuracy at which k₆₀₀ was measured. Here, we calibrated our acoustic measurements against flux chamber-derived estimates of k₆₀₀ using CO₂ as a tracer gas. CO₂ dissolves relatively well in water and therefore strips relatively slowly into bubbles, implying that k₆₀₀ predictions based on our model could be underestimations for gases with lower solubility in bubbly flow (Hall and Madinger 2018). On the other hand, our static flux chamber technique may overestimate k₆₀₀ due to turbulence induced by interactions of the flow with the chamber walls (Lorke et al. 2015). We were not able to reduce this potential error source, e.g., by letting a flux chamber drift freely down the channels because of frequent obstacles, chutes, and narrow passages. However, we regard the risk of our flux chamber technique to overestimate k₆₀₀ to be minor for three reasons: (1) our k₆₀₀ estimates for SB and RI were within the range (1–8 m d⁻¹) measured with drifting chambers in similar surface flow types (Lorke et al. 2015); (2) additional field measurements did not show any enhanced turbulence due to the presence of our flux chamber (Supporting Information Text S4); and (3) in a direct comparison with the tracer gas injection method, our flux chamber technique resulted in 39% lower k₆₀₀ estimates across the whole range of measured k₆₀₀ (Klaus et al. 2018). Together, these comparisons corroborate our k₆₀₀ estimates, keeping in mind that there is no method that provides the “true” k₆₀₀ for comparison.

We evaluated our method across the range of typical k₆₀₀ values estimated in running waters (Wallin et al. 2011, 2018; Raymond et al. 2012; Schelker et al. 2016). The applicability and accuracy of our acoustical method can be expected to increase with ambient flow noise levels and k_600. The method is applicable in turbulent running waters with k₆₀₀ > 1 m d^-1, and best suited in bubbly flow, i.e., standing waves and/or chutes. Such ecosystems are not only hotspots of air–water gas exchange but also show large temporal and spatial variability (Wallin et al. 2011; Hall et al. 2012; Schelker et al. 2016).

Comments and recommendations

We have demonstrated that the sound of running waters contains unique spectral information that can be used to predict k₆₀₀. The relationship between sound spectral properties and air–water gas exchange is conceptualized in Fig. 12, illustrating how sound spectra shift with increasing gas exchange velocities. With faster gas exchange, SPLs rise predominantly at octave bands associated with bubbles both above and under the water surface. Under water, SPLs also rise at octave bands associated with turbulence. This makes underwater recordings superior to aerial recordings in their ability to predict k₆₀₀ and its driving mechanisms. With faster gas exchange, bubble associated SPL peaks also shift toward lower frequencies (Fig. 12). The exact mechanism for this frequency shift is not known, but warrants further research, given that it could indicate a shift in bubble size distributions and bubble coalescence with potential implications for k₆₀₀ (cf. Woolf et al. 2007). Here, a deeper analysis of spectrograms investigating temporal variability in sound spectra across different time scales may reveal exciting new insights into turbulence, bubble, and gas exchange dynamics. Future research should also assess the generality of our framework, by comparisons across a wider range of systems, including standing waters, and calibrations against k₆₀₀ estimates derived from a variety of tracer gases with different solubility and hence affinity to strip into bubbles. Further method development should focus on exploring factors that determine site-specificity of dSPL-k₆₀₀ relationships and the space integration of the acoustic technique. Valuable insights will emerge from work assessing to what extent acoustic signals associated with turbulence and bubbles could be masked by other sound sources such as wind, bedload transport, biological activity, machinery or traffic, and if needed, develop filtering techniques to remove such noise.

Figure 12

Schematic summary of the acoustic signature of air–water gas exchange in running waters, including conceptual spectral diagrams of SPLs across the audible frequency range for conditions of relatively slow and relatively fast gas exchange. Gas exchange velocities increase with turbulence and bubbles. This increase is detectable by increased SPLs associated with air bubbles. Under water, the peak associated with bubble sound shifts toward lower frequencies and additional sound is produced by turbulence. Directions in the shifts in sound signatures with faster gas exchange are indicated by dotted lines with arrowheads.

Our proposed acoustic technique is suitable for continuous monitoring. Long-term outdoor audio recording is possible with minimal calibration efforts (Mennitt and Fristrup 2012). Such data would allow continuous k₆₀₀ determinations that better match the time scale of high-resolution gas concentration measurements. Combined, these techniques would result in improved air–water gas exchange estimates. Another promising application is the discrete snapshot determination of k₆₀₀ across many sites using our cross-site calibration model.

Hydrophones exhibit the unique potential to distinguish between different mechanisms associated with air–water gas exchange. We propose that underwater sound spectra indicate, at least qualitatively, the relative contribution of interfacial and bubble-mediated gas exchange to k₆₀₀ (Fig. 12). Here, hydrophones may be a valuable tool to study the small-scale variability in source contributions that cannot be resolved by the dual tracer gas technique, currently the only method we are aware off to constrain source contributions to k₆₀₀ (Asher and Wanninkhof 1998). To systematically reveal causal factors for variability and quantitatively separate the single effects of turbulence and bubbles on the sound spectral signature and k₆₀₀, combined bubble plume and flume experiments with parallel measurements of turbulence, acoustics, and bubble characteristics would be needed. Such experiments will be useful to establishing physical relationships and developing mechanistic models of k₆₀₀ in running waters. Universal models of k₆₀₀ are currently lacking but would be highly desirable to relieve our dependence on statistical models. Inspiration may come from physical models for turbulence-generated seismic noise (Gimbert et al. 2014). Ultimately, our work encourages future links of existing physical models of bubble- and turbulence-mediated sound (e.g., Manasseh et al. 2008; Bassett et al. 2014; Liu et al. 2017) and bubble- and turbulence-mediated gas exchange (e.g., Lamont and Scott 1970; Chanson 1995; Woolf et al. 2007). Overall, we see great potential in our method to improve the spatiotemporal coverage of gas exchange estimates in running waters with exciting opportunities to better constrain biogeochemical fluxes and ecological processes.

Acknowledgments

We thank Antonio Aguilar, Björn Skoglund, Maria Myrstener, and Sonja Prideaux for field and lab assistance, Diego Tonolla for helpful initial discussions on the study setup, Christer Nilsson for lending the acoustic Doppler velocity meter, and Anders Asplund for providing us the anechoic room at the Division of Speech-Language Pathology, Institute of Clinical Science, Umeå University. We are also grateful for comments of three anonymous reviewers on a previous version of this paper. This work was supported by the Swedish Research Councils Formas (grant 210-2012-1461) and Kempestiftelserna (grant SMK-1240) with grants awarded to Jan Karlsson, and by Stiftelsen J C Kempes Minnes Stipendiefond and Arcums Strategic Resources for affiliated researchers at Umeå University with grants awarded to Marcus Klaus.

Conflict of Interest

None declared.